The new batteries will reverse charge the old almost empty ones.
If they are in series they will all be essentially empty anyway. They may still give a decent voltage with no or little load, but the useful capacity left will be low.
Didn't know reverse charge is a thing. I thought batteries can only be charged using charger...
What do you mean batteries in series? I use 4AA batteries in blood pressure monitor. Is that what you mean rather than using batteries from different devices together?
A battery gets charged any time a voltage higher than the battery’s own voltage is applied to it. It’s something you want to avoid happening by accident, and one way that can happen is when you put batteries with very different charge levels into a device.
Google “series and parallel circuits” to understand what “in series” means. It’s a core principle in electronics.
If you have some cells with a bit of residual charge, save them for infrared remote controls, which generally use very little power and are often perfectly happy with cells that are too low for other devices.
But since remote controls use 2 batteries, I must still make sure batteries of same brand and type are used and both are at the same charge?
I just mean that if you, for example, take 4 batteries out of your blood pressure monitor (which uses motors and thus will require comparatively “strong” batteries) because it won’t run any more, you may be able to use 2 of them in your TV remote for a while. (Put them into a separate small bag, clearly labeled “for remote controls” and only ever take them from the same batch. Do not mix and match batches.)
Just get out of your head the entire idea of mixing batteries from different batches/sources, period. You can’t accurately characterize the used batteries well enough to determine which could theoretically go together, and the monetary savings from doing so are pointlessly small.