European govermnents often have international regulations specifically to make this sort of stuff work more smoothly.

For example, a person living in Germany with German citizenship employed by a Dutch company will have to pay income taxes in The Netherlands. Similarly, they are granted social security under Dutch laws.

In some cases you fall under the employment laws of the country of residence, in other cases under those of the country of the employing company. In some cases it depends on where the work is actually done, and sometimes it even ends up being split between countries.

Fun fact: due to COVID in some cases work done in (for example) Belgium was legally considered to be work done in The Netherlands - as doing otherwise would have some nasty tax implications.

It is also not uncommon for companies to pay taxes in countries besides the one they are legally located in. For example, a webshop in Europe is required to pay sales taxes to the country and according to the laws of the country of the buyer - not the seller.