FYI -- I did a quick search in VAERS for bell's palsy after covid vaccinations and came up with a possible signal for J&J.
Looking specifically at the two-week window between two and four weeks after vaccination:
J&J: 20 / 2.8 million doses = 7 cases per million
Moderna: 30 / 64.3 million doses = 0.5 cases per million
Pfizer: 18 / 69.4 million doses = 0.3 cases per million.
The expected rate in two weeks is about 7 cases per million, but the much lower numbers for Moderna and Pfizer are really a better comparison, since people are probably equally likely to report a problem after each vaccine.
Bell's palsy after vaccination (or infection) doesn't typically show up immediately, and many people aren't going to make the connection between a vaccine they had a month ago and the Bell's palsy now, so it's helpful to have the other vaccines as a comparison group.
Bell's palsy is nowhere near as serious a problem as the blood clots in the brain, but it can be pretty unpleasant. It is much more common in people under 65, and slightly more common in women (both in VAERS and in general).
So if you are risk-averse, the RNA vaccines continue to look like the lowest-risk option. For the needle-phobic, the risk of Bell's palsy with J&J is still pretty low.