New basisPursuit function of MATLAB vs SPGL1 tool for BPDN problem

In R2022a release the new basisPursuit and sensingDictionary functionalities were premiered for solving the BPDN problem.

SPGL1 is a widely used and effective tool for the BPDN.

The motivations for using MATLAB native function rather than external one are:

1. No need to be updated from the external to MATLAB sources
2. Opportunity to use basisPursuit and matchingPursuit within same formulation.

I would want to know if basisPursuit is effective as SPGL1 with respect to the time consumption for each iteration and the number of iterations for a given problem? Can somebody present an example?

Question to MATLAB: SPGL1 has a very useful feature of implementing the sensing procedure as (more efficient) function rather than matrix multiplication. Can this feature be provided by the MATLAB within sensingDictionary too? (It seems to be not a problem, as a handle to a function can be an input like the custom sensing matrix itself).

Another question to MATLAB: can the functionality be transfered to the general MATLAB product from the Wavelet toolbox? BP solution can be widely used for a variety of problems rather than the wavelet decomposition. (Generally speaking, I think that it seems archaic to manage many toolboxes with separate payments... But the MATLAB is still my main instrument of work).