In addition to public computers and physical offices, smartphones are owned by a large portion of homeless people (especially if younger) because they're quite affordable. It looks like a basic Estonian phone plan, plus financing for a budget smartphone, is only 20 EUR/month. Estonia has no free phone plan (like the "obamaphone" program in the US), but low income people can submit 200 EUR of expenses per year for essentials.

I think this just adds the option and doesn't eliminate the in-person version.

You can still go to the office and do it in person. It also comes with the benefit, that a lot of public offices can also provide you with different services they couldn't do previously. Before you needed to go to town A and get a document, add it to the paperwork and file at town B. Now town B can fetch the document in your name from town A, or town A can file the document in your name at town B.

There's basically always the option to use a library or its WiFi. In the case of voting, one can just do it in person.

They can go to the local council / municipality and get the help there (either computers they can use for free, or from the clerks who can help them).