So you use the 3537 for the extension to pay the tax not the annual fee. 

The 2023 annual fee should have been paid as an estimate last year, so unless you need to pay some tax (when their income is over the limit and they owe tax too) you wouldn't need an extension, since no money would be due.

If they didnt pay the fee as an estimate last year, I think it just gets paid when you file the return.

If you want to pay the 2024 estimate now, you'd use 3536.