Convert PSyAd kernels and algorithms into source code - meta issue

### Are there any linked Issues or Pull Requests?

See checklist below.

### Brief description

We've taken the decision to convert the adjoint kernels (and adjoint test algorithms) built by PSyAd into adjoint source code so that they are easier to maintain. This will be done in stages to make things easier to review. This issue will have the sub-issues attached pertaining to the conversion each section. Once the checklist is complete, this can be closed:

Checklist:
- [x] #338
- [x] #408
- [ ] Convert FEM and linear physics PSyAd kernels and algorithms into source code
- [ ] Convert inter function-space PSyAd kernels and algorithms into source code
- [ ] Convert solver PSyAd kernels and algorithms into source code
- [x] #623
- [ ] Remove PSyAd building from adjoint import

### Further details of the issue.

_No response_