Here is what you are missing. With mutations of Covid, the production of antibodies after vaccination drops by a factor of 2.something (Delta variant) and 4 (some African variant, thats not as wide spread yet, partly because its not as contagious as delta). The Delta varient also increased R (the reproduction number) meaning its more contagious, than the original covid, meaning, for herd immunity to work - you'd need higher vaccination percentages in the population (about 85% by now), to also saveguard people that arent vaccinated (children under 5 f.e.).
So here is what happens in a little more detail - mRNA vaccines took the spike protein of the original covid (the one it penetrates your bodies cells with) and designed it onto a malign (useless, not harmfull) influenza virus (one that humans dont even get influenza from). Thats the one you are injected with (if you get a mRNA vaccine) Immune response to that is about 10 fold after full vaccination. Mutation (delta variant) comes along and immune response drops by a factor of two, because delta 'looks different' to the immune system. Drop by a factor of two should still be enough to grant about 40-60% (if I've read that correctly, its early - not enough studies at scale yet) immunity (compaired to the control group - meaning, you have to add a few percent judging on the individual level) and about 80% if you add non symptomatic infection. (Thats the average from mRNA fully vaccinated, and vector vaccines fully vacinated. mRNA vaccines - two shots, should bring you to 90% immunity and or non symptomatic infection.)
Difference: Immunity is when you arent even infectious (not reproducing the virus). Non symptomatic infection is when you are not showing any symptoms, but are still infectious for a while.
Why so many mutations? Basically, because influenza viruses have a tendency to mutate quite fast. (Flu shot has to be adjusted every year.)
Other viruses dont have that tendency. So vaccination great (lifelong immunity, or booster shot every two years or six years, or so). Influenza viruses - as Covid probably needs a booster shot every year. But maybe not, but every two years, ... Booster candidates have already been produced by Pfizer and Moderna, and are currently in evaluation. (State has to decide if it makes sense).
That said - even with 80% asymptomatic infections - it helps in protecting against "grave progression" of illness and "long covid" and you are producing a much lower virus load, so you are less infectious to others.
Hope everythings a bit clearer now.
Aside: We arent reaching 85% or 90% vaccination rate this year (or in some countries ever). So its likely that you'll see increased mitigation measures again this winter (mask wearing, maybe curfews and or quarantines -- with a target (why are we doing this?) not to have emergency rooms overwhelmed). In future years, with vaccines targeting the 'variant (mutation) of the day better' vaccination rate needed might be able to drop to 60-70% again, for the people not getting vaccinated also being protected by a herd effect. We'll see.
How that works: If you have "one person infects three others" in place growth rate is exponential. But if a certain percentage of your population is vaccinated so that growth rate drops to "two people infect one other" propagation is stopped and reversed. So at that point even people not getting vaccinated are protected, by others getting vaccinated, because infection isnt growing anymore, its regressing. But it also is dependant on R (reproduction rate - how many other people is one person infecting, which varies by mutation).
Also: Vaccinations are needed for protection currently - because mutations are so wide spread by the end of this year, that a person already having had Covid is somewhat likely to catch the mutation again.
Two times (mRNA, not needed with Johnson & Johnson f.e. - although I dont know the protection percantage of J&J against the delta varient) vaccinated people (with current vaccines) have a much higher immune response against delta (even though it is halved in effectiveness compared to original covid), than people who already got Covid (old variant) once.
And people who had covid once, and get one shot of mRNA. Are even better off. (Because mRNA boosts antibodies, but they also got T cells immune response, from when they were sick, which apparently is a great combo).
Problematic sideeffects (from mRNA at least) are at 1:700.000 and mostly seen in women (anecdotal, dont trust me on that..

), so the breakdown is: Get vaccinated.
Source: Me reading stuff..

(Newspapers mainly.)