I spent a non-trivial amount of time on this when I was running my businesses.
There are, roughly, three very different rationales to have business succession planning in place, and at the scale of a solo operator they have very different best options available:
1) I want to avoid negatively impacting paying clients in the event of a bus factor issue.
2) I want to avoid negatively impacting "the community" in the event of a bus factor issue.
3) I want to ensure my heirs receive the residual value of the income stream.
#3 is by far the easiest for the typical case: buy more term life insurance than you otherwise would. The end. Most people in this situation are, roughly, young and healthy, and term life is a cheap commodity. If your app is throwing off $50k per year, great, take a few hundred dollars and buy a million dollars of 10 year term life; if you kick the bucket your heirs now have a ~$40k safe withdraw rate. (You can get almost arbitrarily high amounts of term life if you throw the words "business owner" around a lot.)
#1 and #2 are a lot tougher because they require a combination of technical skill, extreme interpersonal trust, non-technical professional labor (lawyers/accountants), non-trivial liquidity, and fast action at what will be an extremely trying time for your loved ones.
The best answer I have for this could fill a small book, but the very short version is that you prepare an In Case Stuff Happens packet for an extremely trusted technical friend who has run a business similar in character to yours, with the understanding that if you are to kick the bucket they will (depending on the nature of the property) either a) if it is a trivial site, put it into "maintenance mode" or b) if it is an active business, prepare it for a quick, orderly sale, or c) if it is in the unfortunate position of being in the goldilocks zone between sustainable-with-trivial-work and economically-viable, prepare it for an orderly shutdown (turn off for new users, announce sunsetting in 12 months, etc).
For more on this topic, you'll want to consult lawyers (who unfortunately won't have all that specific useful advice) and either people running businesses with similar characters who have done it multiple times before (death is just another form of exit ;) ) or business brokers (who specialize in orderly transitions and know what you'll need to have lined up).
