The Home Office has a target to process citizenship applications within 6 months. In most cases this is adhered to.

Timeframes can and do vary from case to case. These days most applications are decided in under 3 months but some may take longer.

Some applicants had to wait over 6 months, in smll number of cases, over a year, however, their applications were successful.
There is no way to track applications nor make enquiries regarding progress.

Once your application is submitted, you just need to wait.

You can't take any action until the allowed six months have elapsed.

If the Home Office needs anything from you, they will contact you.

Please refer to the following update from the government regarding applicants without settled status awaiting a decision or a ceremony

You only become officially British on the day of the ceremony, not when you get your decision letter.

A pending citizenship application or a letter stating your application has been successful do not prove your status in the UK.

If you applied for citizenship with a PR card, these will no longer prove your status in the UK and you will need to apply for settled status.

You can still use the PR card number to apply for settled status, as noted here: Applying with PR

You need to apply for settled status before the end of June 2021.