Covid gap year and grad school admissions
With the COVID pandemic affecting a lot of ways of life, graduate department adcoms are more likely to be understanding of certain abnormalities in transcripts and such when they review them, at least in the immediate upcoming cycles.  These can include having to take classes P/F, as some schools have switched to that grading model as a result of having to go entirely online.  In general also, I don't believe that taking over four years to finish undergrad will be a liability either; even in normal circumstances, things can happen that graduate department adcoms will also understand, such as major changes, having to retake classes after a dismal year, etc.

That said, you will have a gap in your CV come application time, hence the term "gap year."  While you could take a break and "do nothing," a better use of the gap year/semester would be, as you said, to find work or attempt to do a (preferably research) internship.  Most are in the summer, but there are a few, especially in industry, that will take on students for the regular semester.  You mentioned your home environment is difficult, so especially if the pandemic situation improves enough, why not take the time to try and gain experience that could be relevant come time to apply to graduate programs?  If anything, do something that you could brag about to adcoms or your friends rather than spend the semester doing nothing.

Overall though, I do feel that taking a gap semester/year could be beneficial in this case.  Especially if you have just gone through a relatively stressful semester, you could use a longer break before going back into school.