Lower gearing with 15 year old Shimano Ultegra My wife adores her 15 year old Giant TCX Composite (size 44!). Arthritis means no getting out of the saddle for hills.

We've got the standard 52/38 up front and a slightly larger 11/26 at the back. A lot lower gearing is needed.

I had SRAM PG990 (I think) on the back of mine, that had (I think) a maximum 34 , which was great . I don't recall if this required a new rear derailleur cage. I think so.

The wife doesn't mind MTB components, as long as they're around Ultegra spec.
I'd rather invest money in a bike she loves, than spend $5k (Aussie) on a equivalent replacement.

How low can we go?
Switching the rear derailleur to a 9-speed Shimano mountain and the cassette to an 11-34 is the most straightforward in terms of minimal parts changes. It's not the lowest you can go. It leaves you with the high gears you've already got, i.e 52/11, which is not useful for most people, but one of the questions here is exactly how much you're happily willing to take off from the high end of the range. (For most people in this situation, but not everyone, the answer is a lot.)

Switching the crank to a compact 50/34 was the next fashion after standard doubles like she has finally fell out of favor for normal people road bikes. You could do so with or without also doing the above rear end change. The FD and shifter you have should be fine. Most compact cranks you'll find are nominally 10 or 11 speed. To make them work with 9, use tiny chainring spacers. There are many posts here about this.

So-called super-compact cranks with ranges like 30/46 have finally started to become mainstream in the last few years. The nice thing about them is that for many people, 46 represents around the biggest big ring that's actually useful, i.e. in many cases everything beyond that is wasted. They'll work acceptably with your FD. A lot of them are external bearing cranks with chainline specced to work with 135mm rear ends, which isn't a dealbreaker for putting on her bike but is a minor drawback. To avoid this you could get a square taper one like Herse, VO, or IRD. Some of these cranks come in variants with big rings smaller than 46, but these won't play nice with your existing FD and shifter setup.