You might like Wordpress’s themes, they came up with a default theme for every year
i was a web developer from 2015 onwards.
I remember in 2015-2018 twitter was still really cool and so was instagram, so I was asked to do masonry waterfalls of scraped posts to detail brand engagement. Tumblr also did a lot of waterfall layout themes. They sort of live in the dinosaur age in some respects so it is still common to see it there. I don’t think brands like to show off feed pages like this anymore, or they use some plugin instead for a small rotator. It’s no longer hip and i dont think people like being reminded of the hellscape towards the end of the decade ( innocence lost etc ).
Bootstrap was also really popular. We still use it now, but old bootstrap has a distinct look, kind of reminds me of mac stoplight colors for buttons, like button states like green for accept/start red for cancel grey for neutral etc we used their default colors across projects regardless of brand design specs. We don’t really normalize them like that anymore atleast where I work. ( It’s more like everything is now as blank and color-free as possible, besides the links being the brand’s requested color )
Bootstrap v2 ( 2011-2013ish?)
Bootstrap v3
Judging by this yeah I think rounded corner buttons were popular early-mid 2010s. They might have some soft shading or hover/depression effects. Later the normalization became no definition and increasingly square, or just generic href links with no button styling.
Towards the end of 2010s I was getting redesigns involving removing borders and dividers around elements which was the most alarming to me as the categorization of the page would fall apart and be harder on UI/UX. Basically white or black backgrounds where elements had no definition or territory. That is leaning towards the outro though.
Towards the mid-end, parallax scroll backgrounds got really popular for a spell! That actually might be a really fun way to make it dated as we don’t really see it much anymore. Some are very corporate like fancy page section, some are really playful like having a background animation. I have a hard time finding the playful examples but I remember them. Parallax is still around but I don’t see it on like a brand’s wishlist anymore for their site, i think. It feels more like it’s more for hype/short-lived marketing things but that’s my thought. I remember it being bundled into default cms page templates more before.
parallax 1
parallax 2
parallax 3
parallax 4 and similar one
I’d also say… any sort of banner rotator, or towards the end swipers.
Unfortunately i think a lot of these are un-fun as web design got increasingly corporate XD but maybe you can make something fun out of them
memey/prominent web stuff of the time - rage comics, i can has cheezburger, demotivational posters, nyan cat, what does the fox say, hipsters, youtube poops/sfms/gmods, 4chan, knowyourmeme, vine, collegehumor, buzzfeed, bieber and gaga covers/jokes, twilight, star wars. IDK if that will help you think of any design ideas or refs.