Yes, No, Maybe.
"Mucinex" comes in many forms. Several have added decongestants or cough suppressants. These are definitely for temporary use only. 7 days unless a longer term is recommended by your provider.

The "original" Mucinex, only guaifenesin in a long acting formulation, has been used for MANY years. I first encountered the generic long-acting formulation as a prescription 40 years ago to treat persistent ear fluid. When it became non-prescription, Mucinex patented the long-acting version and cornered the market. Now apparently the patent is expired, and there are a few generic extended release formulas of pure guaifenesin around. But the "specialty' versions are still under patent.

Guaifenesin is largely considered safe for extended use, with minimal side effects. I have been looking for any studies demonstrating this, and there don't seem to be any, but here is one that surprised me. It is a case study (one patient) but demonstrates my experience and my husband's (he has GERD & mild bronchiectasis caused by RA) https://www.atsjournals.org/doi/abs/10.1164/ajrccm-conference.2018.197.1_MeetingAbstracts.A2169
In our home, we have fewer exacerbations, looser, more productive coughs & less congestion with guaifenesin. (We are on our second extended-release generic brand, and have found both equivalent to Mucinex.)

If Mucinex works for you, discuss long-term use with your providers. Don't be surprised if they roll their eyes - if they agree it's safe, use it!

Sue