If I plan on taking an international trip early next year (several months from now) but my passport is expiring in a couple months, is there any benefit in renewing it before it expires versus waiting a couple more months? No idea if those extra few months 10 years from now would be of use, but all things equal, might as well.
Each country has different rules regarding passport renewal, and the process normally depends on how recently your passport has expired. eg, if your passport has expired less than 2 years ago you may be able to do a simple "renewal", but if it's more than that then you might have to do a full new application. I would suggest checking with your countries passport office to determine if there is a difference, and how long past the expiry date the change in process occurs.
Otherwise the only real reason for renewing early is that it means that you have a valid passport in your hands. If you have an urgent need to travel for some reason, and your passport has expired (or even, depending on the country you're travelling to, if it has less than 6 months validity remaining) then you will not be able to travel.
If you have renewed it before the 6 month mark, then you're ready to travel at any time if the need arises. If you know that you're not likely to need to travel internationally, then you can hold off until closer to your planned trip.
Consider that renewing your passport will take some time, many weeks if you are unlucky. Then consider that when you renew your passport, something could go wrong and your passport could get lost or your passport application could get lost, so you have another multi week wait after you realise that your passport won't be arriving. I would renew my passport a long time before it is needed.
Also consider that you might want to travel unexpectedly, and your old passport might not be accepted. Some places want a passport that is valid for six months, or you can't enter.
Assuming you don't have any other travel plans in the meantime and assuming your current passport won't cover the trip then exactly when your current passport expires is less of a consideration than when you intend to travel and where you intend to travel to.
A standard US passport application is quoted as "about 6-8 weeks". There is a expidited option but it costs an extra $60 . That is a subtantially greater cost than losing a few months of validity because you renewed earlier than you needed to. I would interpret the "about" as "we don't garuantee this" and would suggest adding some buffer on top (not being a US citizen I don't have a feel for how much)
Also if you need to apply for visas before travelling then it is likely you will need to get your new passport first and you may find it difficult or impossible to paralellise the visa application processes.
So you need to start from your intended travel date and work backwards to figure out when you need to start the application process.
You get a simpler renewal process when the expired passport is less than 15 years old, which would be the case here. What you need to consider is how much time, if any, you need to procure visas. You now get a tracking number when the passport arrives at the central renewal office, and of course you should send it there by registered mail.
Of our last two renewals, one did not arrive anywhere near the promised date, and they expedited it at no charge when we called. The other arrived two weeks early. The queue is much longer in the spring and summer.