TL;DR: when you interact with a custodial service (ie you don't own the privkeys), it is entirely up to that service to 'credit your account' appropriately.
There are many types of Bitcoin wallets, but on a fundamental level we can draw a line between two types of wallets: those that give you access to your private keys (non-custodial), and those that do ...
You can use scantxoutset command which was introduced in Bitcoin Core 0.17. It scans the UTXO set for any UTXOs for the address (or output script) provided. It is faster than the rescan when you import a private key.
Type help scantxoutset to see the help.
If I understand correctly you can use this command getrawtransaction to get a transaction that is in your node's mempool i.e. an unconfirmed transaction.
However, if you are looking for a transaction that has been confirmed, you'll need to know the blockhash of the block in which that transaction resides.
> bitcoin-cli getrawtransaction "...