PCR tests are for free, but take some time, often at least a day. Our health service first didn't want to test for vacations, only for real worries about infections. "We are a health service, not a service for fun stuff". One was supposed to go to a commercial testcentre. The gouvernment did arrange that during July and August one can test for free before going on vacation. Test type depends one the requirements of the country one wants to go to.
Home tests are available, even Lidl has them, for around 2 euro 50 a piece, but they don't give you a travel certificate. Fast tests and home tests both are considered a lot less reliable than PCR tests.
What does worries me is that only 75 percent of the new hospital patients is only half or not at all vaccinated. My rather limited calculating skills do makes that sound like a considerable percentage of patients that are twice jabbed - 1 in 4.
Here we have PCR tests, quick-tests and quick-self-tests. PCR and quick-tests in official places are free, and the PCR results will take a while to come through. Home (self) quick-tests are cheaply available and you don't have to go anywhere for them, but they will not give you a certificate in case you need to prove your covid-free-ness. For that, you have to go get tested.
Since quicktests and home quicktests are the same method, they are about as reliable as each other, and much less so than PCR... so getting a PCR is the thing to do if you want the best test.
The considerable percentage of new hospital admissions that have been vaccinated is, as far as I gather, an effect of a relatively high rate of vaccination combined with the new variant(s) - the more people vaccinated, the higher the percentage of them will be in overall infections and accordingly also in hospital patients. The big question is how severe their illness is, then (presumably still less severe than without the jabs). But yes, having the full vaccination is not a complete protection, and also does not mean that there's no danger of spreading the virus.
Here in the UK: PCR tests are free at the test centre or posted to your home - you post it back free.
Lateral flow tests should be free from an employer, but I don't know how much they're paying for them.
Yes, the vaccine isn't 100%, but it doesn't need to be if enough people have it as the virus will die off or become isolated in pockets if it can't spread. What the vaccine does do is make sure that anyone who does catch it gets a milder version, so they may be in hospital but fewer end up in ICU or dead.
This household is watching the variants closely as we had different vaccines.