How does one know if they solved the block other than a surprise in your wallet???
I can think of three methods in addition to your wallet as you say:
1) I assume you see the surprise in your wallet only after one confirmation or perhaps two confirms (meaning, Blocks solved after your Block), but you can see Blocks getting accepted in real time at sites like:
https://mempool.space/2) Plus, you can also see the stats for your workers/wallet where you'll see a huge number [currently 108+Trillion, but Difficulty changes every two weeks approximately] as your new Best Share. For that go to
https://solo.ckpool.org/users/INSERT-YOUR-WALLET-ADDRESS-HERE3) Lastly, all the pool stats are reset after a Block, so if you check here you can see if the stats are reset:
https://solo.ckpool.org/pool/