Right, so there are three elements here (let's call them #1, energy, #2, plants, #3, animals)
TS=(Digestibility OR “energy content” OR “Nutritive value” OR “forage quality” OR “nutritional value“ OR “energy intake”)
TS=(flower* OR leaf OR leaves OR litter OR branch OR branches OR twigs OR stem OR stems OR seeds OR seed OR fruit OR fruits)
TS=(“herbivor*” OR “ungulate*” OR “mammals” OR “grazer*” OR “browser*” OR "mix-feeder*” OR “livestock” OR “domestic animals” OR “captive animals”)
With no filters, in WoS Core Collection, I get 107k results for #1, 3023k results for #2, 270k results for #3. (Yours may differ depending on exactly which bits of the Core Collection your institution subscribes to).
Combined - #1 AND #2 AND #3 - I only get 1245, which is much more reasonable. But not the same as you were getting - why? You mentioned in the comments that you were searching All Databases rather than Core Collection.
Trying again in All Databases, I get 265k results for #1, 8490k for #2, 19019k(!!) for #3. And combined, 22532 results. So, we can see the problem here is driven by using All Databases. But why?
Normally, when you search a single database like Core Collection, you are only searching the Core Collection metadata for each article. This is not always as useful as you will find in other databases - eg MEDLINE might have really rich and detailed subject headings, but Core Collection will just have a few keywords.
An "all databases" search will search the metadata in all of them - MEDLINE, BIOSIS, Core Collection, and so on. It thus leverages metadata that only exists in one database even if the paper is found in several different ones - which can be really powerful, or can be really treacherous.
In this case, it's treacherous. You'll note that we get 2.5x as many for "energy", 2.5x as many for "plants", but 70x as many for "animals". So what's up with "animals"?
Web of Science "all databases" includes BIOSIS (if you have a subscription to it). If you open up a paper's record in BIOSIS, you'll see that it includes extensive keyword/subject heading data. This is from the first paper I picked out which matches the "animal" part of your query - it's about congestion charging in China.
Because BIOSIS is structured in a very logical taxonomic way, this paper - and millions like it - will be returned by any search for animals, primates, vertebrates, mammals, etc. And your search includes the keyword "mammals". Bingo. That keyword is massively inflating the results for your third section, and as a result a lot of papers that match parts #1 and #2 but you would not expect to match #3 are showing up as valid matches for all sections.
Drop out "mammals" and we go down to 473k results for that part in all databases, final results 3395 - much more reasonable and in line with the other results. The Core Collection search gives us 145k results for the animals search without "mammals", 1139 overall.