I'm a long-time Berliner, spent more time here than anywhere else in my life. Most people in Berlin have a love-hate relationship with the place: it has some huge advantages and can give you a lovely lifestyle, but it has some very, very annoying aspects too.
Most people who come here from other countries cope fine, some don't and have to leave. The best thing would be if you set yourself an initial period of a year to try things out and make a long-term decision after that.
Yes, international companies based here are crying out for experienced tech people, you'll find a job pretty easily. Make sure the job is as an Angestellte (staff member) rather than a freelancer. Employers pay half your health and pension contributions, so that makes a big difference to the final income, but it's also a lot easier bureaucratically.
A lot of people have mentioned health insurance, for good reason. The system costs more but it's ultimately not in permanent crisis like the NHS. It's wise to get into the state system (gesetzliche Versicherung) because you pay a fixed proportion of your income, whatever health issues come up or however old you are. In the private system you might have certain advantages like priority appointments and private rooms in hospital, but you also pay according to how much of a risk you are, which obviously increases as you get older and develop more chronic conditions. Someone above mentioned the danger that the state system might not want to let you in at your age: just talk to someone from one of the insurance agencies about that. It might be the case that if you can prove you were hitherto insured in the UK by the NHS (ie not privately insured beforehand) you will be allowed to get state insurance - that worked with me many years ago. The health agency I would recommend is the Techniker Krankenkasse, because they insure a high prorportion of graduates who tend to have a higher income, so they tend to be nicer on the phone. Avoid the AOK like the plague, they're dreadful.
Accommodation: are you thinking of a flat in the centre or somewhere more out in the burbs? Prices have gone up hugely over recent years, but you should still manage to find a decent renovated 2-room place in Mitte for 1500 euros (including heating). Two rooms would mean one bedroom and one living room, plus bathroom and kitchen. We spent a long time in the inner city and then felt the need to move somewhere on the outskirts with less dog poo on the streets. At your age and with adult kids I'd prefer to get a nicely renovated Altbau on a leafy side street in Mitte or Prenzlauer Berg. 4th floor but with an elevator <gasp> because I'm that decadent, and if I'm being really picky one room (living room) to the front of the building and the bedroom to the rear. Oh yeah, and air conditioning - the magic thing that is much needed but nobody in Berlin is prepared to admit is necessary.
Socialising and fitting in: don't see why that should be a problem if you work out what your interests are and then join a Verein (club/association). There's a Verein here for most things. You might prefer places where you can talk in German to practice, but there are also a few active international associations, precisely for women in your postion:
Women's International Club Berlin Women's International Club
International Women in Berlin
Weather: you must know about this from your son. The weather is shocking here. Freezing cold in winter and horribly sticky hot in summer, with a few between days separating the two. In recent years there's been essentially zero winter and unbearable summers, it's got way worse since I moved here. We're getting air conditioning put in upstairs this year, and will probably go to eco-hell for it.
Oh yeah, oil and gas, that's another joyful topic. Almost all of Berlin is heated with oil or gas, much of that is Russian. If you can find an apartment with some alternative form of heating (maybe hot air from politicians?, grab it quick. We're trying to negotiate heat pumps being installed - for 2023, because there's literally no appointments left this year. Do check how your new apartment is being heated