Of course you can pin and follow hastags in Mastodon.
- Search for a hashtag (e.g. #web in the search bar).
- Click on the hashtag (#web here, as an example).
- You will see a column #web open in the web interface at the far end.
- You can pin this hashtag column by clicking on the three settings leavers at the top of the hashtag column, then selecting Pin.
It may be worth thinking about how/where could this be implemented in the simple interface… as a future improvement.