Agreed, there are a lot of problems with the search on the transactions feed. Other banks let you specify any arbitrary date range, it’s annoying not to be able to in Monzo.
There have been many requests over the years for improvements to the search, but unfortunately nothing has happened. At one point several years ago, it even looked like there were plans forming for a great search feature, but alas nothing seems to have come of them. 
If you have a search on the forum for improve search or something similar, you’ll find many threads. I hope Monzo do eventually address this, search really lets the app down. You can’t even do something basic (and extremely useful) like searching for 20 and having transactions with a value of 20 in them come up (like £20.13 or £13.20).