Basically, if you get vaccinated, you're safer.
But no one else is, even from you.
TL;DR: Nope. You can hang around other vaccinated people and be less terrified when you go places because *you* have a low chance of getting severely ill or dying. But not them.
So, people who have been fully vaccinated are less likely to be infected by the virus and much less likely to be symptomatic / have severe illness.
If vaxxed ppl are infected and asymptomatic, there was a recent paper that shows they emit about 75% less infectious virus/ID50s* than an unvax person.
That's still a lot of virus.
People who haven't been vaccinated are still fully vulnerable, of course.
So, if you as a vaccinated person are around someone who's unvax, there's less of a chance you'll have the virus to give them, or to give them the virus if you are asymptomatically infected, and they'll have a lower initial viral load if you do. This probably correlates to less severe disease or later onset. We don't actually know which or even if this is accurate, but it's logical and generally true for most other viruses.
However, a person emitting 75% fewer virions in an enclosed room for 2 hours is still going to fill the room with 1500 ID50s in 2 hours, if they don't cough at all. It won't be 6000 ID50s like if they were unvax. But 1500 ID50s will definitely get people sick. (IIRC, a single cough from someone with influenza has about 100 ID50s. Each normal exhale has about 5 ID50s. 10 bpm * 2h.)
But it's always a dice roll. Every time an unvax person is around anyone for a short time outside or to a lesser extent fomites, it's a dice roll as to whether they're going to get sick. And if they do, then they'll have a 33% chance of long-term complications and a 5-ish% chance of dying, just like normal.
The benefit is that they'll have to roll a 1 or a 2 on a 6-sided die to get sick, instead of getting sick if they roll a 1-5.
But if they roll a 1 or a 2, they're going to get sick.
And as a vax person, if you're infected, there's less of a chance you'll know it.
Vaccination helps the vaccinated, only marginally the unvaccinated until we hit 70-80% vax population levels. Even then, we're going to have localized outbreaks probably spread by asymptomatic, vaxxed carriers.
I'm sorry I can't just be “Woo hoo fly and be free!” but it's not realistic.
And BTW, the rapid and PCR tests do not tell you if you're “safe” to be around other people. The Covid tests can tell you, after 5 days of symptoms, whether what you have is Covid or not, and even then there's a 20% false-negative rate. If you're asymptomatic or pre-symptomatic, which means if you are not actively sick, the false-negative rate is up to 100%.
Hugs and stay well!
*ID50 is an Infectious Dose sufficient to sicken 50% of the population, because some people are my husband who could probably fight off the bubonic plague, and some people are me who gets sick walking through an airport every time. An ID50 for influenza is 2000-3000 virions.