The popups are created by the site you visit. As you have noted, you
won't change, so you suffer what content they choose to deliver. It's
their site, their content.
You never mentioned if you use an adblocker extension. I use uBlock
Origin which subscribes to 11 blacklists (the ones that I choose, not to
all available). I use Firefox x64 90.0.2 on Windows 10 Home x64 21H1.
I see no popups that you describe; however, a site may not always show
their popups or CSS pages on a visit, and instead trigger based on when
you last visited, like they'll show their popups once per day.
I have not seen the popup from Google trying to lure you to their Chrome
web browser from quite a while. I don't know if that is due to my
settings in Firefox or by using the uBO extension. After Microsoft
dropped their EdgeHTML rendering engine to go to Blink (Google) and
dropped their Javascript engine to switch to V8 (Google), extensions for
Chrome can also be installed in C-Edge (Chromium Edge), so I also have
uBO installed in C-Edge.
I would have to test for many days, if not weeks, to check I no longer
get Google's plea popup to switch to Chrome to know if my Firefox setup
and uBO extension is causing the block of the popup, or if Google simply
decided not to nuisance me, anymore. I'm in the USA, so that can also
affect when the GDPR nuisances appear. GDPR is more EU crap.
The cookies, and the prompt to have you accept them, is due to the GDPR
regulations regarding privacy; see:
https://en.wikipedia.org/wiki/General_Data_Protection_Regulation
The effect by the gov't in protecting your privacy is you get nuisanced
with trivial popups rather than getting users educated on the available
technologies, like how to purge locally cached data from the web browser
on its exit. Firefox already has the purge-on-exit options. With
Chrome, you have to install an add-on, like Click&Clean. The gov't
figures citizens are as stupid as they are. It isn't just Google
showing the popup to accept cookies. LOTS of sites that try to use
cookies will show their popup, or an overlay that you have to click away
to see the web page content underneath. It's how they indemnify
themselves against the GDPR.
By the way, you can use the Google search engine without using the
Google web site. Some online search engines anonymously submit the
search criteria to the Google search engine, but the site presents its
own web page of results. I use ixQuick's Startpage, because, like, you,
I find Google's search results more pertinent. I don't use their
extension in Firefox, but just define a bookmark with the keyword "s"
that submits
https://www.startpage.com/do/search?q=%s, where %s is the
placeholder for the search string you specify, like entering in the
address bar "s intel i8700". You can also make Startpage the default
search provider in the web browser. No, you aren't switching away from
using Google to do the searches. You are still using Google, but
switching away from using Google's home page which consequently gets rid
of any popup coding that Google employs at their site. You can use
different frontends to Google's search.
"Startpage.com has a contract with Google that allows us to use their
official "Syndicated Web Search" feed, ..."
(from Startpage's FAQs)