I'll focus on the "gig" aspect primarily.
I doubt that this will occur and sincerely hope that it doesn't. The problem is that the gig economy is explicitly exploitive of its workers. It is designed that way, actually.
Those who try to make a living as an adjunct (most commonly in teaching courses), need to juggle around five different positions in order to make a minimal living. The pay is incredibly low in the US and there are no guaranteed benefits for part time workers. No health coverage. No pension. No say in university policies unless there is a union.
Some people teach as adjuncts because they already have a highly paid position elsewhere and just want some connection to students and faculty. For them, the money (or lack of it) means nothing. Some of them might get involved in research with other faculty, but don't depend on that for income. It is a hobby in some sense, though I know people who do it well. The "win" for them is in the connections, nothing more.
To try to extend this to a research career, juggling several gigs, seems impossible. The problem, at base, is that it is difficult to do real research on a part time basis. If you are working on a problem (I'm thinking math, actually), you don't normally turn off your brain to move on to the next gig after the two hours you've allocated to this gig. So, you wind up self-exploiting if you really do the research right and the employer is probably counting on that.
There are some positions that might be available in grant funded existing labs, especially for specialists. These are more likely to be short term, rather than part time, I'd think. Hired for a particular task within a larger one. But that has always been a possibility. And there is no possibility it can be done remotely in many fields.
To expand to the other aspects of the question, not that in some fields you don't need to be co-located to do research together. Many of my papers are with widely separated (several continents) colleagues. What is needed is the ability to communicate and that is possible now. But my university wouldn't have been willing to hire any of my co authors unless they moved to this location. One of the reasons has to do with law. But the bigger issue is that a university has a diverse mission. Even R1 universities have a teaching mission, including undergraduate in almost all cases. That is much harder to arrange remotely and still fulfill all employment regulations. And again, it is a special problem for part time work (in US) as such work seldom comes with the normal benefits that let you build a career in a non-exploitive way. I'd guess some of this will/does occur, but don't expect it to become standard.
Finally note that one of the key characteristics of a university is that it is a community. It is why universities want students (and faculty) back on campus as early as can be arranged. Partaking of that community is extremely difficult at a distance and impossible for a gig faculty worker. Thus, for students, the "college experience" is lost at a distance and the collaboration "serendipity" of the coffee lounge is lost for faculty. These are very important, even if somewhat intangible.
There is little joy or satisfaction in a completely transactional relationship.
