As Dan says, its pilots discretion as to whether they will fly close or through thunderstorms.
You can expect delays I’m afraid if the weather is in or around the airfield.
Planes fly out of the normal routes to avoid cells which vastly increases work load on ATC.
To help manage the work load and keep the planes seperated (3miles or 1000ft), flow restrictions on departures and arrivals can be implemented and holding in the air takes place.
In effect the size of the airspace becomes smaller because we can’t use it all, so therefore less planes can fit in it.
I’ve had inbounds to London airports hold for 30 min then divert to Amsterdam or Manchester. Even had a wizzair turn round and go back to Budapest!
Weather is when the job is at its most stressful.