Having graded what feels like a million pages of homework, I have seen a connection between writing content and writing style. I can tell if the writing is writing in a hurry when the penmanship is sloppy and their thoughts are undercooked. I've also seen some absolutely atrocious handwriting which I swear was written with a left foot wearing a mitten. You're handwriting is fine.
As we've all transitioned online, I've also become self-conscious about how my educational content looks on camera. Speaking only for myself, I decided that as long as it's readable, you're fine. The extra effort required to make it beautiful "Disney quality" will likely require more time than you're willing to invest.
(I did pre-print some of my content with some funny fonts for some limited purpose, so as to save time in having my students watch me write it out. They are empowered to slow down the video or even pause it if I'm going too fast.)
There's my $0.02. :)