Non-software-engineers may not realize that the process described, is indeed, exactly how all modern software works.
The most common phrase you hear today is ...
Or you will hear aphorisms along the lines ... "in software you might do something twice, but you'll only ever do something three times, once!"
You always trade "more work now" to avoid work in the future. Every time - always.
This applies on the biggest imaginable industry scales ("the baas revolution" is, precisely, that), and on the smallest working scales (you might write a extension to "double a number" rather than laboriously typing that out each time).
Note! that' Tom's exact, specific literal example:
... install some software on a few PCs. It'll take you a few minutes per PC. Or you could create an automated system, which is more efficient in the long run...
Note that there are, literally, massive companies (with 100s of staff) which, do literally nothing other than addressing that specific problem! Automating "installing software on PCs".
It is a massive, billion dollar issue in large corporations. (Indeed, a trivial everyday example - every person reading this uses the "software installation and update" stuff on the common phone platforms, every day: those systems are incredibly complex and have 1000s of engineers working on it.) An absolutely exact example of the "automate everything!" dictum.
Now finally, to answer Tom's question: sure, you can imagine someone going crazy and spending days automating something - where it was overkill!
Indeed the best term there is
The many other suggestions here (circuitous, tortuous, long-winded etc) are not really correct - because they don't capture the idea that, indeed, automation is the normal, correct "thing" (software engineering "simply is" "automate everything", that "is" software engineering).
"Overkill" completely implies that
"...in this case..."
you went to far.
Regarding the terms like circuitous, tortuous, long-winded etc. Say you were indeed writing some software. (ie: you were automating something. that's all software is.) Within that effort, your code may be (in a word) "bad", it may be long-winded, tortuous etc. In that context, you would use terms such as circuitous, tortuous, long-winded and those are the commonly used terms for precisely that.
However, it does not really parse to describe "automating something" (ie .. "making software") as circuitous, tortuous, long-winded if it was a case of "unnecessary automation": the only term I can really think of for "unnecessary" automation (or "unnecessary" anything) is "overkill".
As a final somewhat confusing point: almost all software engineers, now, and for say 10 years at least, agree that - quite simply - it's literally impossible to automate too much. Automation is just never wrong. (The whole point of, say, the whole "open source" fiasco is that you automate every little thing, and throw it up on github so that, well, one by one ever little thing becomes instant to get done.)