I travel on BA from the US to Europe, through Heathrow, with a group of about 20 cycling friends every year. About half of them notify BA about their bikes, and half don’t. We’ve been doing this for more than 20 years. It never seems to make a difference.
i have never deflated my tires. I have personally ridden my 100 p.s.i. tires to over 14,000 feet in elevation, with no problem. Certainly, aircraft are pressurized to approximately 7,000 feet elevation, so it is not an issue.
My only advice to flying cyclists: Put an AirTag in your bike box.