Using the mirror nodes is the recommended way to check if an account is currently associated with an HTS token. It’s important to note when you associate with a token it will show you have a 0 balance of that token. Once you receive that token your balance will go up as expected.
Here is how you can check using the mirror nodes:
First, construct a fetch request to get account info by account id.
const testnetUrl = 'https://testnet.mirrornode.hedera.com/';
// fetch the account info
const accountInfo = await fetch(`${testnetUrl}api/v1/accounts/${accountId}`, {method: "GET"});
convert the response to json and grab the associated tokens list from the json
const associatedTokensList = accountInfoJson.balance.tokens;
Here is a link to the Hedera Mirror Node REST API swagger documentation
https://testnet.mirrornode.hedera.com/api/v1/docs/#/