kw - may be a Q for your insurers.
Fairly common for building owners to get buildings surveyed e.g. every 5 years, though like most such things the timings should be chosen according to condition, likely speed of deterioration and the potential outcome should something go wrong, amongst other variable.
So this means deciding not only how often to do inspections but how to do them, which might vary inspection by inspection.
As example if your structure was a trunk road, there are specific standards adopted by each of the four Highways agencies in the UK.
Every 6 years (unless otherwise decided) every single structure on the trunk road network has to have a "Principal Inspection" which is more in depth that inspections in between.
At the turn of the century I found myself standing inside a quite famous bridge, which has voids inside each of its pillars. The standard for a Principal Inspection said at the time (though it has since been somewhat amended) that a Principal Inspection involved a competent engineer or similar getting within "touching distance" of every part of the structure. On that bridge this meant building a scaffold down each of the pillars - so putting quite a lot of people not only at risk of falling (as just one of the risks) whilst erecting and dismantling each scaffold but also exacerbating any confined spaces risks within the bridge. On any normal day for one or two people standing inside the main part of the bridge there would be plenty of fresh air or even a howling gale! But not in those voids lower down. I don't actually know what the inspection protocol now is for that quiet famous bridge but it might include remote inspection for some Principal Inspections.
Same priniciples apply to your Grade 1 chimney stacks. May be you need to send the drones up sometimes but erect full height scaffolding from time to time to have a closer look, especially if your drone footage indicates concerns. BUTTT, your Grade 1 building might be in the middle of nowhere and you might decide that the population at risk was so small that the expense of building scaffolding was not merited, or at least not as often.
This is one for a structural engineer or building surveyor and not just any old engineer or surveyor but one with an understanding of how historic structures work. Your Grade 1 structure is VERY unlikely to have been built to Eurocodes and it is quite likely that some engineer brought up on Eurocodes might be horrified by its method of construction - yet it has stood there for possibly hundreds of years and nothing has fallen down in the meantime!
....and as to the population at risk you need to consider not only who they are but when they are present. If as example you let visitors in, this is likely to be during daytime hours. You might decide that if a chimney stack is going to collapse it will happen when there are high winds at night, or even high winds from a North Easterly direction (i.e. the direct opposite of the prevailing wind in the UK) at night i.e. when the visitors are miles away sleeping in their beds. So chimney stack falls down but nobody anywhere near, so hits the press but more a drama than a genuine "near miss".
Further, you might assess where the product of collapse might fall and fence off an area alongside a building rather than shutting down all access. Horses for courses (including courses of chmney stack brick or blocks).