This was about to go alongside my seasonal gripe about gift as a transitive verb (We already have the word give!), but from your examples it seems it's already an established niche usage in the scientific community in the context of vaccination. I'm dubious about the usages outside that context, though...

I think "booster" should only be used when it is ambiguous as to whether the text is referring to inoculation or not, but then again I'm not an expert.

There’s also bolster

@AndyBonner But isn't regift mainly a verb?

Specialized contexts often use unusual or variegated forms derived from the same root. To booster has a specific meaning and context where to boost would be confusing. Rather like rob versus steal, where the object is different, though the event reported is identical.

@JohnLawler So "to booster their morale" should be avoided? Dictionaries seem to ignore booster as a verb entirely.

Well, of course they do. It just popped up last year. What do you expect from harmless drudges?

@JohnLawler They should adopt my late father's philosophy: start at perfection and work your way up.

Necessity is the mother of invention. New terminology, new usages follow complex major upheavals like wars, pandemics, breakthroughs in technology ... and follow quickly. 'Boostered' is best kept for 'given the booster injection' (though there are those with underlying health risks who have been triple-jabbed but not boostered).

Google "get boostered" to find a lot of matches. Many of them before 2019, so not related to the COVID19 vaccines. For example, canine parovirus: "...and then adult dogs will get boostered every one to three years."

@TinfoilHat "boostered" alone returns 328,000. I think the verb/adjective, well established in the scientific community, is starting to make its way into everyday speech with the pandemic.

“boosted” “vaccine” (12,800,000) vs “boostered” “vaccine” (79,200). And then look at the context and the sources. If I were an animal vet, maybe are boostered would be okay (it appears to be vet jargon). But I'm an editor. So unless you're a vet — no.

@TinfoilHat The headline Google total is always inaccurate. 1. say No to "Did you mean XYZ"? 2. at the bottom of the page, click the last number. At the bottom of that page you see "..., we have omitted some entries very similar to the XXX already displayed. If you like, you can repeat the search with the omitted results included." (Doing that usually doubles the number of results). The real results are “get boosted” vaccine (167); “get boostered" vaccine (182) “got boosted” vaccine (85) and “got boostered” vaccine (76). the other search terms are included in the latter.

@TinfoilHat Thanks. The current usage in news media will IMO be a big influence on usage going forward. IMO. In the transcript to a Dec 15 White House covid-team briefing Dr. Walensky used "boosted" about five times if memory serves; Dr. Fauci used "boosted" once and "boostered" once. // I've reformatted my question to separate the other meaning, "to promote," and I've added examples.

@Greybeard: I have no idea where you are getting those numbers; without and with omitted results for “got boosted” vaccine — for example — yields 8,930 and 8,990 respectively. And the omitted results are literal duplicates of articles already returned.

From the CDC: Get Boosted!. These examples are incorrect: booster their self-confidence, booster their capacity, booster their shoreline defenses, booster their moral intention. Of your examples where the verbified booster means advocate, the ones where booster is followed by for are incorrect. The others are correct enough if you accept non-standard, ad hoc verbs. Consider, for example, the verb advocate and the noun advocate from which it comes. They are both clearly standard. Booster is not there yet.

@TinfoilHat If you choose to use booster as a verb meaning promote, why can't you booster for a club or city? What makes this usage incorrect?

For the same reason that using for after the verb advocate is incorrect. You can booster a club (if you accept verbification) but not booster for a club.

@TinfoilHat If I say I'm using it to mean "root," does it suddenly make it correct because you can say "root for" a team? Four of the "ad hoc" usages are "booster for." // The OED has several citations for "advocate for"

@TinfoilHat In fact, the OED for advocate has "intransitive in same sense. Chiefly with for".

As I mentioned, I'm an editor (not a descriptivist). Advocacy English