Interesting, trying it out on Discord the default max msg size is 2000 chars and with Discord Nitro the max is raised to 4000 chars.

Testing with Postgres, a 2000 char random sequence doesn't result in TOASTing, but a 4000 random sequence does get TOASTed

And for kicks, 4000 chars that aren't random compress well enough that they don't end up in TOAST.