Years ago, I set up https://mitmproxy.org on a Raspberry Pi and used it to get logs of every site that my kids would visit. I should be clear that monitoring/spying != parenting, but it definitely made me feel a little better to have some idea of what the kids are using the internet for.

From a technical perspective, it did exactly what you want. I had logs of full urls (not just domains). So, for example, I could view what they googled and when, if I wanted to anyway.

It did involve installing a certificate on the computer that they use, but there are how-to guides so setting everything up was simply a matter of following instructions.

The biggest drawback is that it noticeably slowed their internet. I imagine if I had run this on a more powerful computer it may have been better.

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Note, for those suggesting PiHole, it is very good for getting logs of domains accessed, but not very informative. For example, you can tell that a computer accessed "youtube.com" at a certain time, but not what was actually viewed. That may be obvious to many of us, but just clarifying in case it is not obvious to the OP.