Handbags   (The sad, the bad and the ugly. Non-productive stuff here.)

I think it is probably more to do with your browser and the settings which are selected, rather than to do with the laptop per se.

Sometimes, I do use a laptop, and the appearance of the screen is almost identical to the large screen that I use with desktop PC. (Very slight difference as laptop's toolbar has icons to do with battery and coms, which are not relevant to desktop.)

Don't use ME, so cannot comment on that Browser.

Google are really chasing advertising revenue at present, so is likely users will notice ads more.

'Firefox' is very popular and allegedly is not harvesting you data to feed to advertisers.

Your description though sounds like the ads are part of the content of the web sites you are visiting. You could try an Ad Blocker browser extension, but some sites rely on the ads to fund them, and not all will function fully if you block their ads.