Need mesh flooring to bring shower floor height up to entry threshold (3.5 inches).

I'm not sure leaving adequate spacing between decking for good drainage would work well for the shower chair wheels, depending on the wheel size. If you needed to increase spacing for better drainage taking the decking boards back up and adjusting the spacing is more difficult than drilling a few more holes in the plywood and mat layer. You would still need a solid layer under the 2"x4"s to distribute the weight evenly to the shower pan. There are several variations on building the insert that would work slightly better and/or look more attractive. The design I choose to document is easy and cheap, requiring only basic handyman skills. If you have the skills and the shower chair wheels are large enough, I would prefer the composite decking too.

Techie I never thought of building a wooden platform but I think that would work very well as a temporary solution. I wonder if the composite decking lumber would be a better option than wood, and perhaps laying deck boards across 2X4 supports would allow for better drainage down to the pan 🤔

Best option would be to install a barrier free (or roll in) shower stall or shower pan (costs $1800 and $400 respectively). If the current shower is tiled, replacing just the pan is possible.

A minimum threshold shower stall/pan with a 3/4" to 1-1/4" threshold along with 3"-4" wide threshold ramp is workable for certain levels of disability and costs <$1000. The person or their assistant has to be strong enough to push the chair over the threshold in a controlled manner.

A quick and temporary solution would be to construct a wooden insert customized to the current shower stall, particularly since you are concerned the current shower pan may not support the point stress of the chair casters.

(1) Find a non-slip mat you can cut down to the size of the shower pan with a little extra covering the shower threshold .
(2) Using 3/4" plywood, cut a lower insert to fit the shower pan and cut out an opening around the shower drain. If the insert cannot make good near continuous solid contact with the shower pan, I suggest using sand placed into panty hose to fill the space. You want to transfer weight uniformly from the insert to the shower pan and floor structure.
(3) Using 3/4" plywood, cut a upper insert to fit the shower pan at the desired height (level with the current shower threshold).
(4) Cut down 2"x4" or 2"x2" to make a lattice support frame between the two shower inserts. This can be as simple as nested rectangles or squares: larger square close to the insert edges, small square about 2" larger than the drain, and 1 or 2 additional squares to place between the largest and smallest squares with no more than 6"-8" between any two squares/rectangles.
(5) Cut or rout several small openings on the bottom side of the support frames to allow the passage of water. Be generous with the number and size of the openings but leave at least 50% of the support frame intact to touch the bottom insert.
(6) Paint everything with a good exterior or water repelling paint or sealant to seal the wood; mildew resistant would be good too.
(7) Place the lower insert in the shower and lay out the support squares with the routed openings on the bottom side. Take a pencil and outline the squares once you have them in place. Using a good mildew and mold resistant silicon sealant, apply a thin layer of sealant to the bottom of the support square pieces and place them on the bottom insert. Don't worry if you cannot exactly place the pieces initially. You will be able move the pieces into place after placing all of them for several minutes before the sealant dries enough to prevent movement. Make sure the sealant does not block the routed drainage openings.
(8) Let the sealant holding the support squares firmly set.
(9) Using a rule, draw outlines of the support squares on the bottom side of the upper insert.
(10) Attach the mat to the top of the upper insert with flat head galvanized wood screws around the outside of the mat; ideally screws are not longer than 1/2" more than the mat depth. You may need to use washers if screw heads are too small to securely attach the mat. For larger screw widths, holes should be pre-drilled before screw placement. The screw heads should compress the mat slightly and be below the mat surface.
(11) From the bottom side of the upper insert, drill 1/4" holes through the insert and mat, avoiding areas outlined where the supports will rest. Make sure you discard all wood dust and mat debris from this process.
(12) Lay the upper insert on top the lower insert and support frame. Turn on the shower and confirm water can flow through the insert and into the shower drain. If water is pooling, drill more drainage holes and try again until water drains freely.
(13) Apply thin sealant film to support squares and place the upper insert in position. All the sealant to dry completely and trim the mat to lay across the shower threshold to meet your outside shower ramp.

I agree with Country Mouse. I think it would be better to have the stall floor brought up to floor level. I say this because, I see u having problems with water draining out onto the floor if the stall floor isn't grated correctly.

When there is a tub involved, there are shower chairs where part of the chair goes in the tub. The chair itself is outside the tub. You sit the person on the the chair and then slide the chair into the tub. Don't see why this wouldn't work for a 3 inch lip. Here's what I am talking about. You probably can find one thats a little cheaper and not so bulky. Just giving u an idea.

https://www.walmart.com/ip/Drive-Medical-Folding-Universal-Sliding-Transfer-Bench/19616138?wmlspartner=wlpa&selectedSellerId=1129&adid=22222222227014964702&wl0=&wl1=g&wl2=t&wl3=40754352632&wl4=aud-834279575926:pla-78607047752&wl5=9003829&wl6=&wl7=&wl8=&wl9=pla&wl10=112562632&wl11=online&wl12=19616138&veh=sem&gclid=CjwKCAiApOvwBRBUEiwAcZGdGHhJL_lxm_mKGiRJPc8Qf51LL8xyb9FwTdHI_h_rdQMWmoGrTIVEhhoCvM4QAvD_BwE

I've been doing a little web searching and I wonder if the "permeable mesh pavers" meant for driveways would work?
(please do let us know if you find a solution)

The potential problem I can see is that the mesh also needs to be very permeable or else the water will merely collect in the open grid and overflow rather than empty down the drain. Another consideration that stymied me in my own efforts to find a solution to this problem is that the floor pan of the existing shower, especially the edges, wasn't designed to handle the concentrated weight of a wheelchair - I feared that the pan would crack with repeated use.
I'm afraid that for her last few months living at home my mother had to make due with sponge baths - Isn't it amazing how difficult even a 3" barrier can be?

Would this work

https://www.discountramps.com/wheelchair/ramps/threshold/p/Thresh-4/?gclid=CjwKCAiApOvwBRBUEiwAcZGdGFoRAvLsyFqTbacDclwqugM1W6zkga5FK-gLPV0J2oajpCkgI45sjBoCF-EQAvD_BwE

If you Google "shower trays for wheelchair users" you'll see a lot of accessible options. I'm guessing it will be quicker and easier in the long run to replace the shower floor/stall than to adapt it, and it will certainly avoid the difficulties you often get with modifications such as mould growing in inconvenient places, things slipping out of place and unforeseen technical hitches.

How long have you got for this project?

Have you looked into flooring for commercial kitchens? They are a grate that allows for fluids to fall through so that people don't slip on them. The flooring is hosed off at night. It should work in a shower. You'll want to lift it up when not in use so that it dries out.