You have a couple of approaches available, neither is perfect, but should help find them:
The spell tag: Control
D&D Beyond adds some metadata to the spells it lists, including spell tags. Forced movement falls under Control, but does a couple of other things (such as preventing movement, etc.). Do note that D&D Beyond's tagging isn't perfect; eg. gravity fissure doesn't have the Control tag, and encode thoughts is tagged as a Wizard spell. You can use this in combination with the other features of the spell listing, such as classes, schools, and levels.
D&D Beyond's general search
For searching through the spell description text, you can use D&D Beyond's general search (found in the top bar) and filter only to spells (click on the big spells icon). Example for "pulled" here. The search is fairly simple, but works well for keywords which aren't too common. You'd need a separate search for each keyword, and this method won't catch spells which has this effect without using a wording you expected. Note that it's limited to 35 results, so if more than 35 spells contain the word you searched for, you won't find all of them.