Will probably be a bit opposite of many opinions on here and though I appreciate Rick Beato I have not seen that vid, I have my own opinions about string gauge though I am not alone in my opinion.
First, I like thinner gauges on electrics 9-42 and my preference is firstly based on TONE. Not feel. In fact it is easier for me to pick on thicker gauges as the tension is more taut and there is less back and forth play on the picked string. That last part isn’t opinion, it’s science, though I really feel once you are used to either it isn’t a huge deal as I will also sometime pick out over the neck pup where tension is looser.
But the tone of a thinner string is different than a thicker string and in my opinion, better. I personally do not like the sound of thick strings on electric. This opinion is shared by many people I know and also guys like EVH (RIP) used 9-40 Fender Bullets on early Van Halen and I read where he said he preferred the tone of lighter strings. Andy Wood talks about this exact subject here on this site in his interview. Billy Gibbons swears by lighter strings, uses 7s and 8s. On acoustics I like 12-53 but it’s a different beast, you need to get that top vibrating to produce the best acoustic tone and volume. And I find it easier to pick fast on acoustic because of the thicker strings.
There is a vocal, singing quality to thinner strings as well as a spunky tone to the wound strings of the thinner sets as they are more prone to a secondary bounce off of the fret producing a brighter attack, great for rhythm and producing a harmonic which is also great for long notes.
I personally believe it is the more pronounced bounce off the fret which helps produce a harmonic and the tone that many like from using thinner gauges.