I design enterprise software and this problem has come up many times.
Firstly if your users want a different and simplified UX, you don't need to provide those features in your Primary Search.
For Primary Search keep it simple - one simple search box is all you need (think Google).
For all those other features you mentioned, create an Advanced Search link and place it on your Primary Search page. When users click this Advanced Search link you can take them to a new page which has all those more complex Boolean search and Save features.
You can now monitor how many people click the Advanced Search link. You might find that not many people will use the Advanced Search, so you can make the Advanced Search page as complicated as you like.
Because you are not an UX Expert, don't take my word of this. Jakob Nielsen is a very respected expert in the field of UX and he said this about Advanced Search in 1997: https://www.nngroup.com/articles/search-and-you-may-find/
(the emphasis is mine)
Boolean search should be avoided since all experience shows that users
cannot use it correctly. We have studied many groups of users who have
been given tasks like this: You have the following pets:
Find information about your pets.
Almost all users will enter the query cats AND dogs. In our studies, they typically do not find anything, since the site never mentions both animals on the same page. Upon encountering a "no hits found"message, the vast majority of users concludes that there is no information available about these pets.
Experienced programmers normally use the same erroneous query, but when they get the null result, they typically say "oh, yes, I should have used an OR instead of the AND."
Unfortunately, most users have not been taught debugging, so they are very poor at query reformulation. This is why I recommend minimal use of scoped search and no use of Boolean search in the primary search interface.
Advanced search is fine if offered on a different page than the simple
search. The advanced search page can provide a variety of fancy
options, including Booleans, scopes, and various parametric searches
(e.g., only find pages added or changed after a certain date).
It is important to use an intimidating name like "advanced search" to
scare off novice users from getting into the page and hurting
Search is one of the few cases where I do recommend shaping the user's behaviour by intimidation.
Jakob has validated this many times since 1997.
Peter Morville is a very respected expert on search and findability, and has identified many search patterns. I highly recommend you read Search Patterns: Design for Discovery by Peter Morville & Jeffery Callender. They say this about Advanced Search:
A relative concept, advanced search includes whatever simple search
doesn't. It's a pattern that many of us love to hate. often, advanced
search is a clumsy add-on that's rarely used, and it lets engineers
and designers take the easy way out.
Is it a user-friendly query builder for novices or a power tool for
This pattern also suffers from an ignorance of context.
In conclusion, advanced search is a pattern on the edge. In practice,
it's often abused and rarely used. Yet, like federated search, it
invites us to go further in our search for ideas, and serves as a
forgiving playground for experiments and exploration.