A solar gravitational lens will be humanity's most powerful telescope (2022)

There have been plans drawn up for space telescopes flying in formation to do the same kind of interferometry thing as the Keck observatory.

The problem is that even far from the Earth, there are tiny but significant forces pushing the space telescopes around. Solar wind, outgassing, gravitational influences from planets, etc...

The precision required to maintain formation is... challenging.

E.g.: https://arxiv.org/abs/1907.09583

Why do you need to maintain formation? Can the just fly randomly and fix the problem storing the info and a software that gets the positions and calculate the delays?

For radio frequency I think it's possible.

For visible light, I guess you must do the interference using very accurate mirrors to aim to the central point and that move slightly forward and backward to get the correct phase shift. I think it's not impossible, but very difficult.

You might be able to capture the phase information for very long IR wavelengths using something like Rapid Single Flux Quantum (RSFQ) circuitry, but I doubt it would be practical. One issue would be that the data volume would be absurd, likely petabytes per second. Practical observations where this would be useful would require long integration times of many hours.

In systems like https://en.wikipedia.org/wiki/Very_Large_Array , do they use the phase information to join the data from different antenas? '

Yes, but at radio frequencies, where the data rate is much lower than with visible light.