appears offline to my friend

Hi Sewey

There is two ways too appear offline it's through the toggle in the Social App or in the Privacy settings i'd check both if i was you. Actually Sewey i believe the way to change your privacy settings too appear online is a Xbox 360 option i don't believe
the Xbox one carried that feature over so if you still own your 360 check there first in the privacy settings if you don't own a 360 anymore you can change it on the Xbox website.

Hi and thanks for reaching Microsoft Xbox gamer's community. My name is Josef.
I'm an Independent Advisor and a Microsoft Xbox user like you.

Hope you're doing great today despite this Steve

Is this issue happening only with this specific friend? Or if you ask to another friend to invite you the other person see your account as disconnected as well?

If not, this can be a bit dumb. But may I know if you tried to delete and re-add this friend from your list?
(Ask her to do the same with you)
After that check if you can play with her

By the way, is she playing on PC Bedrock or she is using a different platform?

You may be appearing offline.

Go to "Friends" then go down to "My Profile". Once there, click "Appear offline" and change it to "Appear online".

All of my friends are appearing offline.

Put yourself online then do a full shutdown on the settings of the xbox a d it should fix it...