[...I believe I covered all this bit I snipped... Rather more tongue-in-cheek about pure robotic repair, but haptic feedback might be much more developed these days.]
For all that the Space Shuttle had serious problems, THIS is the sort of capability it had. In order to replicate it you need more than a space capsule.
I also regret its retirement, though it arguably delayed other developments in the US space program (covered by the Soviet-as-was one, but even they did quite a lot for the
arguably better Buran, which got just one unmanned flight before mothballed/roof-collapsed.
It's possible to build a vehicle on-orbit (which I wish somebody would do) capable of executing the plane changes and maneuvers and the like (ion thrusters to maneuver around, anyone? Just maneuver while there's no crew on board and the months it takes you don't matter) and carrying the airlocks and crew space and manipulator arms and EVA suits and spare parts and all.
Which orbit? The one Hubble is in? Or what will eventually become the transfer-orbit to Hubble - hopefully to be met by the manned flight that still has to match it in the same trajectory as it is about to make its way to the Hubble rendezvous, then burn to match Hubble for everyone to work then reverse that to get everyone back to Earth (wherever you leave the repair-station, unmanned again)...
If they can't LEM-like the EVA/manipulator adapter with the Crew Dragon, for size/weight reasons, then indeed send up such a tin-can separately, but it wouldn't (especially with dedicated rocketry allowing it to be larger without the bag of humans on its tip) need to be of a size needing orbital pre-assembly (yes, something that would be useful to do, at some point, but not for this), but could certainly be equipped with a Shuttle-Arm/Canadarm (without needing the travelling rails across strut-segments, or even any travelling capabilities) or three for heavy 'lifting' or man-platforming where EMU/MMUing is not possible.
Docking with the human-lifter should be enough assembly to still give a 'station' with camp-out pre-EVA facilities and airlock. The single connector in use during heavy orbital adjustments may need to be more robust than the more passively-orbitting ISS ones, though they clearly survive trash-avoidance and decay-delaying manouvers, plus Nauka's thruster-error which spun the station all the way around and more and I think there's not much more problem for a planned, in-line reboosting stress. At both ends of the transfer (and maybe back) of the combined unit.
The other big alternative is capturing Hubble (safely, remotely) and bringing it to ISS (or ISS levels), before reboosting, but I'd be more scared of its fragility than of a sevicing crew and their vessel.
(I'm all very pro-Starship as an idea, but I can't see it being used to help Hubble soon enough. This all arose from having had Inspiration demonstrate the wherewithall to at least reach the right sort of apogee, the first manned craft to do so since the shuttle mission on the last Hubble-repair, everyone else since then has only ever visited the ISS or the new Chinese one, that went into orbit at all. Even at SpaceX development speeds, and Muskite perserverence, I'm not sure they'll get a fully capable Starship up there soon enough to be Shuttle 3.0.)
edit:
But bear in mind the Russian modules. And other non-US ones, but Russia (maybe for their own reasons) are also starting to talk loud about how the use-by-dates on their current bits are passing, or passed already, with smoke alarms having sounded. And their newest addition, just this year, malfunctioned and spun the station round 540-odd degrees before its thrusters ran out of fuel and the attitude could finally be corrected.
It's only a matter of time before some hopefully not too severe emergency causes even bigger problems. But then also I'm afeared for the first big public accidents for the space-tourist efforts (probably going to happen for one or other of the current big three corporations, rather than Russia if they even restart that side of things[1], before the market gets too many more players into active service).
[1] Their vehicles, if not their modules, are generally good quality (rogue holes in cargo modules aside!) and have proven launch-escape survivability when the rockets go wrong. Plus they haven't been sending tourists up since they used the seats involved only for ISS expedition crewmembers. Theoretically Dragon's ISS crew-servicing could free those back up again for those who might make the same safety assessment for me but also have the money to burn on such a jaunt.
...didn't feel like adding as a (new) new post, but it's now out of order and repetitive.
Editedit:...aaaand I'm wrong on one point, already. Soyuz MS-19 is about to blast up with a Russian actor and actress (no non-Russians! ...which might be the first time for Soyuz for yonks) so they are taking 'tourists'.