How do you get a unguided timed entry into st. peter's basilica

You don't.

Everyone who goes into St. Peter's waits in line for the security check. There is no skipping that line.

Your best bet is to get there early. It opens at 7am every morning except Wednesday.

It is free to enter.

New for this year you can buy an audioguide that includes access to a shorter security queue. In March, the only slowdown in that queue was the nun in front of me who slightly struggled taking off her jacket. https://www.basilicasanpietro.va/en/products

Take binoculars to look at the “paintings” they’re mosaics.

Are you able to just tour the basilica on your own, after going thru security, without buying the audio guide?

Yes
You can tour on your own

It seems you have to pay for the audio guide to get access to the shorter security line. You don't have to use the audio guide, but paying for it should save considerable time. I am a real cheapskate, but I'd pay for that audioguide without a second thought, whether I intended to listen to it or not. You won't believe how long the regular security line is, unless you plan to show up before 7 AM. It was so awful in March 2024 that I took one look and said, "No way". That was before they set up the audio guide option.