What does the application you use to interface with the blockchain have to do with integration? The mobile/desktop application is not the integration point, the blockchain itself is.

Individual application integration is pointless, especially given that you can use the same mnemonic/passphrase with multiple applications at once (not a good idea, but can be done). And should those applications use the same derivation path, you will see the same address, transactions, and balance. Or in the case of ETH, MATIC, BSC, etc; then you just need to add each blockchain individually with the same receiving address and it will import.

The mobile/desktop application you use is merely an interface/GUI for interacting with the blockchain, it doesn't contain your crypto. Your crypto is never actually "in your pocket", only your keys and access to your crypto is. Really, no different than the currency in your traditional bank account is not in your pocket, despite you having a debit/credit card and/or mobile app with access to it, the currency is still sitting at the bank (really, its just on the banks computers, they don't actually have every account holders balance in physical currency at the individual branches).

The "wallet" in the names of these mobile/desktop applications ("safemoon wallet", "fearless wallet", "trust wallet", "exodus wallet", etc) is a misnomer. They really should be called interface apps.

Now, if you are talking about the safemoon BEP20 token, then you would just add your BSC receiving address to the respective blockchain in koinly and it should bring it in. Binance Smart Chain is already integrated.