I recall a video promoting EN, that handwritten notes/picture, takes longer for Basic Users to get search results, from OCR. But that premium users, don't have the same length of delay. Perhaps the same philosophy is occurring here with Text only searches, for basic users (replies are from premium users). That I, as a Basic User, get my sync'd searches returned much later than you, premium subscriptions. If that is the case, basic vs premium, we're comparing Apples and Oranges with regards to time to sync Text notes, into searches and turn around sync times.
Perhaps I need to adjust my expectations as a non-subscription user (if my hypothesis is correct). My needs are rather basic, with only 30 notes or so. But it makes it difficult to explain to a fellow non-sub beginner user (my 70 year old mother), if I have to tell them, "trust me, your text search will work tomorrow". Her possible Response: "but Google Docs works/searches immediately, and I can access it from both the phone, and my PC, and I just put them in Google Drive folders... , and I can search ". Seems pretty reasonable.
Yes, a forced Sync seems entirely logical, every other app free or premium out there has that feature. Perhaps for a Basic user, limit a forced Search Sync to 2 times a day. Possibly, the feature doesn't exist to push basic users to buy premium. Really, I don't need immediate text syncing, its just that was trying to learn/test the syntax type search, by completing/uncompleting checklists/checkboxes, and saving the effective search into my Saved Searches.
BTW, they really should do a better job of handling single Checkboxes, and have a menu item, for each, currently the windows button is for checklists only.
Want to have a beginner roll their eyes and discount EN? Then instruct them to do a single checkbox (not checklist), that they need to add a space, then insert a '[' and a ']', (keys they've never used before), to manually get a single checkbox, green outline, and tell them to ignore that glaring button on the toolbar (windows), that shows a checklist, since that won't work for a single checkbox. Then tell them that some of their text search results will work later that day, or maybe tomorrow.
Forced Sync & single checkbox button (that doesn't convert into a checklist). Probably been said many times before.