Best way to self custody different coins?

Hi all, this is my first crypto cycle and as a newbie I would appreciate an advice on storing my crypto keys.

I bought into a few mid-cap projects and at this point I want to move my assets from the exchange into (ideally) a cold wallet.

I had Trezor or Ledger in mind, but quickly realised none of the cold wallets support all of the assets I have. I had a look into hot wallets and equally couldn't find any that would support all my assets. Is that normal? Would I simply need to have 3 different wallets to store all my crypto or am I missing something?

If this is indeed the case it seems quite annoying, having to flipflop between the wallets, instead of having everything in one place.

Also probably worth mentioning I don't intend to stake, trade or do anything with my crypto, just hold it in a wallet.

Any advice would be appreciated.

Thanks