No, this is not plagiarism. This was amply explained by the other answers, so let me instead address the question of which pieces of advice to acknowledge in your thesis.
The dilemma I face is that it feels somewhat awkward to cite internet
pages such as Wikipedia or forums, or to include individuals’ names in
citations.
When you thank people you don’t cite them. You just add a footnote or a remark in the acknowledgments section saying something like (depending on your style) “The author / I / we are grateful to … for drawing our attention to the paper [17]“.
This makes sense to do if you are thanking a specific person who gave you good advice specifically tailored to your situation. It does not generally speaking make much sense to thank people for things you read on Wikipedia or in a book or on a forum (unless a specific user gave you specific useful advice), though certainly it makes sense to say “I am grateful to the users of MathWeb for sharing their expertise on topic XYZ” if you feel like it. It is also unnecessary to thank people in your thesis for pointing you towards a reference which is widely (though perhaps not universally) known your research community.
You have no obligation to track precisely the chain of references which led you to the result you were looking for, but I would think it is good manners to acknowledge people who gave you useful, specific advice, especially since it doesn’t cost you anything. (Probably you don’t need to do this in your thesis with things that were pointed out to you by your advisor, provided that you appropriately thank them in the acknowledgments section.)
For people who gave you small but useful pieces of advice (“you should check out paper [34], it sounds like it could be relevant to your work”), you could just collectively thank them in the acknowledgments section instead of specifically pinpointing which person pointed you to which paper. For people who suggested a book, I would in most cases not thank them explicitly for this, unless it is a truly obscure book.
Whether the person giving you advice is Prof. Mountainson, leading expert on mountains, or forum user suckmycloaca326 should not matter in principle, although I think everybody would understand your reluctance to explicitly acknowledge the latter. In particular, if someone on MathOverflow or Math StackExchange helped you get unstuck in your research, then surely they deserve to be acknowledged, no matter how silly their username is (you could even ask them for their real name if you want to avoid mentioning their username).