Are there any small, public matrix spaces or rooms for just meeting and chatting with people, making friends and such?

Depending on the instance you're on, you should be able to search for some public rooms.

You can also try and find spaces of spaces. There are people who create "indexes" of the public spaces that exist, by creating spaces, to which they then add other spaces. You can then share invites to that big space containing a bunch of spaces, and it can be used as a list for finding stuff.

Here's one containing a bunch of public spaces for finnish-speaking people

https://matrix.to/#/#offtopic-space:envs.net contains a list of off-topic/general rooms, most are not so big (less than 20 active users). See also https://joinmatrix.org/guide/popular-rooms/.