feat(web): attach composer state drawers#7150

fix(web): hide unavailable task toggle

fix(web): keep task progress current

fix(web): polish composer task controls

feat(web): show live composer tasks

feat(composer): show skill source icons

fix(web): use shared stash button styles

fix(web): keep stash access beside drawers

fix(web): join external composer drawers

fix(web): keep attached stash controls reachable

fix(web): preserve composer drawer access

fix(web): match composer stack surfaces

feat(web): add compact composer button size

fix(web): preserve composer drawer fallback

feat(web): attach composer state drawers