Make solvers more uniform

A few points that need to be adressed

- [x] Use implicit updating of the different linear operators instead of recreating one at each iteration #274
- [x] Solve the arrow issue when verbose > 0 across solvers #234
- [x] Use the callback variable for the doc: #234
- [ ] Replace `\nu` in R2 with `\sigma k` (like `R2N` and `R2DH`) : #232
- [x] Make it so that solvers do `n` iterations when `max_iter = n` instead of `n+1`, also move `get_status` from `src/R2_alg.jl` to `src/utils.jl` #233
- [ ] Solve the issue with the way the step length is computed in `TRDH/LMTR`, see https://github.com/JuliaSmoothOptimizers/RegularizedOptimization.jl/pull/199#discussion_r2263123939_