Starting point has got to be checking the battery open circuit voltage. So, after a reasonable run, say half an hour, to charge the battery, let the car stand for a couple of hours to let the surface charge dissipate from the plates. You can achieve a similar effect by turning the headlights on for 5 to 10 minutes if you're in a hurry but many modern vehicles won't let heavy loads - head lights, rear screen heater, etc - be turned on unless the engine is running. Then, without starting the engine or turning any electrical load on, check the battery voltage with a voltmeter/multimeter. If you decide to do this then post the result on here and we'll all have a think about the result.
Like Baglady, If I'm in a car with stop/start I turn it off every time I start up in sympathy with the starter motor/battery/flywheel ring gear/avoiding localized boiling of coolant/turbo/and other stuff which doesn't come to mind at the moment. So, for me, I take failure of the stop/start as an early warning to check battery condition and if that's ok then the the fact stop/start isn't kicking in is a bonus!
EDIT Just because it's such a commonly reported failure, I'd have a quick look at the gearbox earth strap (under the battery box) for evidence of rot, but it's unlikely to be the problem if the engine is starting normally and the car is working well in all other respects. You could also try your local Halfords and ask if they'll do a free battery condition check for you - ours is happy to do this. This procedure is very quick and involves using a battery condition analyser to check the battery's internal cell resistance. The result gives you a much better idea of the battery condition than any simple test you can do at home - unless you have a condition analyser yourself?
Here's the "DIY" one Gendan does in case anyone is interested:
https://www.gendan.co.uk/product_FXBT100.html And just to show I'm not biased, another that interests me greatly is the Topdon BT 200:
https://www.topdon.com/products/battery-tester-bt200