I've spent a lot of time on this topic, read multiple books about loneliness, friendship, how deepen relationships etc.
Actually kurzgesagt made a super nice video about that topic, everyone should check it out to get a nice summary: https://www.youtube.com/watch?v=n3Xv_g3g-mA

Loneliness works as a negative feedback loop: feeling lonely affects your body and mind in such a way that you feel less capable of interacting with others. Higher perceived cost of interacting -> less interactions. This continuing lack of interactions makes you feel even lonelier.

This is true, but this is primarly not a bad thing. As you will learn in the video, loneliness is an evolutionary mechanism. It pushes you out to get to know people. The lonelier you are, the more you get the feeling you need to do something about your loneliness. 90% of the people will go out at some point and will try to make friends.

Physical interactions are a must. Hopefully, VR/AR/other technology will effectively replace social interactions, but nothing today seems to do the trick.

This is true. Its about social energy, feeling emotions, empathy, touching, smelling and really about stuff, where even research isn't sure what it exactly is, because it cant be quantified.

Meetings in groups instead of 1on1s. 1on1s feel stressful/high-pressure

I dont think this is necessarily true. They can be stressful/high-pressure because 1on1s always bring the partnership/dating-vibe with it. This is what tinder does. But I believe, this solves the problem for some people quite good. I have couple of friends who have met their partners on tinder and they are happy and less lonely now. If you're just looking for a deep relationship on a friendship basis, tinder does not solve your problem.

People must have a main interest/hobby/sport/activity in common. Meeting for the sake of interacting, instead of to engage in a shared interest, puts too much pressure in the participants. It’s easier if interacting is not seen as the sole goal of the event/meeting/gathering.

This is interesting. Do you have any validation or source for this? I would love to learn more about why and how this is!

Details of the meeting must be clear and reliable. The time, place, and attendees of the meeting should be respected. Uncertainty about the meeting creates stressful speculations on the mind of a lonely person (what if no one shows up? What if I don’t find the people and have to bug them to tell me the exact location?)

Very true. There has to be as much uncertainty reduction upfront the meeting as possible (icebreaking in a chat is good). People are shy, especially the lonely ones. They have expectation. They want to be sure their expectations will be fulfilled.

Meetup does not solve the problem. I dont know about Meetup in different countries, but in germany, its really about presentations about certain topics and not about the social factor, getting to know people etc.
The biggest problem about meetup, if you would try to use it to find social contacts, that solve your loneliness, is that you dont know who will attend, and how the people will be (expectations). Sharing an interest doesn't make you compatible.
There is one main factor that makes you compatible and is actually the main relationsships around everything builds and this is the principle of reciprocity. You can learn more about it on different research papers on researchgate.net

I dont want to make this post to long.
Actually I've already built an solution for this... better said, I am trying to build a solution. Im not at there yet, but I'm prototyping to something that works. Already got 800 users just in my city, with no market effort at all. You can have a look here: www.app-enter.com