Melanie, if I may call you that, feel free to always enjoy and appreciate the ones who throw you some kindness. You deserve it with all the fantastic talent you possess, especially in the creation of wonderful music and visual novels :)
The webdev work is a gift, it has been already covered so 'but thou must' and no excuses! :)
I wish I was as popular as you are getting as many messages and having trouble keeping up. I run a Discord server but it isn't exactly poppin off as often as I'd like even after 5+ years of being online.
I suppose my only advice I can offer is to let people know that you cannot keep up with every message or respond to every person. Perhaps you could do a 'Q&A' response post for those who support you via itch.io donations or ko-fi or otherwise. One of the things about being a celebrity (even on the internet) is that you do what you can within a reasonable timeframe. Burnout can happen and often has happened to content creators on YT and other parts of the net.
I remember back when JaidenAnimations (yes, the real one) on YT was just starting out and barely getting 5k views on a video (closer to 500) and I'm like 'this girl is GOOD and she's gonna be amazing I hope someday' and not only was I right but she's getting 20+ million views a video plus several million subs plus merchandise plus events plus all the other stuff. She connected with other creators (per my suggestion so long ago that 'networking is important') and from there she really took off doing collabs and other bits (again, stuff I suggested as part of networking with others). She used to be super duper shy but I'm really happy for her. Many celebrities end up becoming hostile/arrogant or think they are better than others but Jaiden is one of the few I can point to and go 'yeah she's legit' and be happy for her success. I sadly don't have the emails we used to exchange that long ago; wish I'd kept them but I ditched an old gmail account because reasons. Use other email that's far more secure :)
What I do personally is keep several emails. I have my Google email only for Google Play stuff on my phone and nothing else. I have two Protonmail accounts, one for strictly IRL and one for strictly online-only accounts that don't have any of my payment or other IRL info. I use virtual credit cards linked to my bank account with most online storefronts to maintain both some level of privacy and a bit of pseudo-anonymity. The email service 'Tutanoga' is also a great alternative, but I like Protonmail since they also do ProtonVPN and ProtonDrive and other stuff all in the same account, effectively an open-source secure alternative to the Google ecosystem.
So uh TLDR I suppose: read as many messages as you can, respond to those who financially support you and your work (within reason, maybe limit to first 100 people by date/time when message is sent), maybe ask Spaghetti to set up a contact form on your upcoming website so you can receive emails easier. I know you aren't much of a fan of Discord and instant-messaging, but doing a once-monthly Q&A live voice thing with special Discord roles on your server with your supporters would be a nice gesture. Let them ask you questions and you answer to the best of your ability, etc.