The maximum number of suits you can own in Odyssey is… (including display bugs)

One hundred, including the flight suit. And only since update 5.

The bugs:
The Codex will only update if you relog and shows you the actual correct number. There is a discrepancy though between the pioneer supplies preview window and the codex, so yes I counted them manually. Thankfully grade 1, 2, 3 sorting and manufacturer sorting helped with counting 🙂

When you open the manufacturing names and mouse over individual ones like Remlok, then it shows you 6 Maverick Suits " + XX more". That number is off by 1, same with Supratech and Manticore. This makes it appear as if you have 3 more suits than you actually have. However, if you mouse over "all manufacturers" I get 6 random suit names and " + 95 more" which is only off by 1 from the total of 100. I don't know where in the counting code the +1 issue happens, but it is.

Despite the codex only updating upon relogging, the game will stop you immediately from buying the 101st suit. My guess is FDev thought 100 is a good number because 3 suits x 33 + 1 flight suit that you can't change sounds about as round as it can get. Yes you can have more than 33 suits in one category as long as you are less or equal to 100 total. And 33 suits per type is more than enough to have a selection to downsize from.

"HOW?!"
I didn't just buy all G1 suits. I was flying around semi-afk with Apex ever since Odyssey started and checked stations as I do on some days, and buy the excess stuff. And this limit I only realized today, the first day of playing after Update 5 hit. I wanted to buy a suit and it refused. I had 188 prior to that, and those were all Grade 2 and 3. So I had to downsize substantially and then raise up as I hit the "hey I can buy again!" threshold with Grade 1.

"WHY?!"
Just like I have ~480 Sidewinders littered among as many systems to figure out the limit is 500 ships per galaxy (phrasing from ingame), I wanted to see where the limit of suits was. Prior to update 5, it looked like it would be 500, but then update 5 happend and… oh well 🙂 at least now that means this test came to an end.

Weapons do not seem to have a limit or I have not yet reached it with around 124 Grade 2+3. They are also not listed in the Codex, so maybe unless that happens the sky is the limit 🙂