HMRC will eventually sort the situation, however, you have confused yourself.
To register as self employed you either set up a BTA or you send in a CWF 1, You do not need to do both!
That said, as you now have a tax record that says you are self employed everything to do with taxes for that will now be done via your annual self assessment tax return. You do not need to do anything else.
Taking your comments at face value, you have SE gross income of 4 k. I doubt you have many costs to deduct from that, so should claim the trading allowance instead. That leaves you with 3k of net taxable profit.
That level of profit is too small to trigger Class 4 NI and, significantly, it is also below the small profits threshold which would give you an automatic "free" credit for Class 2.
Do you understand that Class 2 is what gives the self employed an NI history entitling them to the state pension?
For the SE who do not get the automatic credit it is therefore necessary for them to manually decide if they want to voluntarily pay Class 2 so as to get that credit. You may not want to pay Class 2 if, for example, your main income is from an employee job where you earn enough that you pay NI on that employee job and get your pension credit via that.
If they want to pay, then they do so via their tax return by ticking the box that asks if they want to pay Class 2! The payment is then made as part of their tax return total owed. (If 4k comprises your only income for the entire tax year then you would have no income tax or Class 4 to pay leaving you only with the choice of voluntarily paying Class 2, or not.
(As an aside, I note your comment re potential false self employed. The penalties for getting that wrong rests entirely with your employer. that said, if HMRC decide your should be an employee, not SE, then HMRC can legally still chase you for any personal tax you may owe calculated at employee rather than SE rates.
Getting your employer to foot that personal tax bill would be a personal legal dispute between you and your employer. You would owe HMRC some tax, they don't care if you or your employer pays it, but they will make sure one of you does.
I appreciate you need an income and this is the "job" that gives it, but if you genuinely think this is false self employment then things could easily bite you down the line)
you will find this useful, and in respect of falsehoods pay particular attention to the page linked off it covering the status checker.
Self-employment: registering for tax and NIC | Low Incomes Tax Reform Group