You've done nothing wrong OP.
Some people have issues but can mask them initially.
After you've displayed a small amount of social connection/positive interest they tend to treat you as an unpaid therapist.
I try to screen people and keep boundaries up for a few months now, see how things pan out in a group environment
She may be upset.
However, I find this type of person often knows they're intense/needy - they don't want to change themselves though, they just find a new person to talk at.
If you make the effort to have an honest conversation/suggest alternative support they aren't interested.
I have a similar relative.
A lot of people (me included) have given a lot of time/energy/money to support them socially and improve their mental health.
But they don't acknowledge this or try to move forward.
They want a 1-1 "friend" to commit to agreeing with everything they say and validate their (petty and unreasonable and self-inflicted) grievances.
They can have Ok moments but its incredibly draining spending time with them, trying to help, but knowing from experience they are going to be exactly the same next time.
It would probably depend on the general mode and frequency of communication as to how to handle this.
If you're not in touch lots anyway a random message might be a bit OTT and pompous.
I agree with some general message like you "have a lot on so can't socialise, but wish her well".