Just to clarify that point all the interior and exterior bulbs are not led but standard spec.
Looking at the condition of some of them they look to be the original 14 year old bulbs.
I’m leaning towards battery as well but will try more investigating before chucking £100 at a new one.
if i may that as there ordinary bulbs is good replacing the interior bulbs with led ones to save ur battery , along with being brighter
will find a link for u
plus if u do end up with a new battery, this is what many of us have been fitting
https://www.tayna.co.uk/EA1000-Exide-Premium-Car-Battery-017TE-P7488.html
plse let us know how u get on, will be interesting to see what they find on ur alternator