None that are affordable or 100% accurate. There are services that will run a DNA test that can look at a set of DNA markers, and then you can compare those to the markers of a known plant. If there are difference in markers, you have determined that the plants are not the same. If the markers are the same you can say the plants are closely related. It is possible to map the entire genome, but at the moment it is extremely expensive. And to identify a plant down to the cultivar level you'd have to map all known cultivars to find a match.

Yes: there would have to be the genetic features of all the relevant ornamental plant selections previously recorded. Otherwise there is nothing to compare to. And with something like hostas where hobbyists continue to generate yet more varieties all the time DNA sampling would have to be done pretty often in order to keep up.

That's why keeping labels on plants is still important. People soon forget the variety, or someone sells their place and it's a new owner.

especially if the plant is a rare variety and worthy of being recognized.

Absent labels, you would have to go through the tedious process of taking pictures of the fruits/flowers and getting responses from experts who specialize in that specific type of plant, in one of these forums.

Highly doubtful that you are going to be able to identify any one single expert who can identify the varieties of all your different types of plants for you. Most garden experts tend to have particular areas of expertise (like roses, or apples).

What you are suggesting doesn't seem very economically feasible. I mean, genetic tests are getting very routine and less expensive these days, but they're still not so cheap it would make sense to use them to identify routine garden plants in someone's yard. On top of that, to identify something from a genetic test, you have to have a database, with many samples from many different varieties already tested. I don't think anyone has even created a database like that. That would have to be a very large database, probably with lots of people contributing, because I doubt any one person or entity has all those plant varieties.

Absent labels, you would have to go through the tedious process of taking pictures of the fruits/flowers and getting responses from experts who specialize in that specific type of plant, in one of these forums.

That's the not the full extent of what can - or should - be done. There is also the studying of web pages and printed references, making in person comparisons of cut samples with labeled specimens in collections and at nurseries.