[tevake]

The lost stuck anchor is a bummer.
You can pull yourself down an anchor line quite a bit deeper than you can free dive. Then pull it out of the obstruction.
Having mask snorkle and fins aboard is good.

If you know you are anchoring in a bottom that could snag the anchor, attaching a line to the bottom of the anchor with a float on it will give you another chance of pulling it out.

Or if you have to leave it behind. You could leave a float on it and come back with scuba gear to pick it up.

So many chances to learn about the intricacies of boating, keep at it and have fun.

I hope your mechanic comes thru for you.

Cheers Richard