If you need to ask random people on the internet what gears you need, the answer is almost certainly ‘as low as you can achieve’.
You will need at least a medium cage derailleur to cope with a 34 biggest cog on your cassette, and a compact chainset (34 tooth small ring). To cope with a bigger cassette & longer chain you will (probably) need a wolftooth (mentioned above), or a grx rear derailleur. The latter will probably get you up to a 40tooth cog, but it is beyond the official spec. I’ve run this with a 50-34 up front with no problems.
I’m 10 years younger, 15kg lighter and ride hills totalling 4000m+ almost every week. My lowest gear is 30 (front) 32 (back) and I use it frequently. The chainset & front detailleur are grx to handle the small chainring.
Edit: apologies, the op wasn’t asking what gears were needed, rather if a 40 could be fitted.