Is my monitor inhibiting my post processing?

Yes, No, Maybe, but it's not as simple as you imply.

I recently acquired a 32 inch 4K monitor and it's nice for the price ($400). It doesn't support high frame rates required for gaming but it handles photos nicely.

However:

The 16 million colors thing comes from 8-bits each of Red/Green/Blue for a total of 24-bits, or 2^24 which is 16 million (more or less). The billion colors thing comes from 10-bits per each R/G/B. You would need a graphics card capable of 10-bit color. You would need to be working in RAW. You would need a monitor capable of 10-bit color. The first two requirements are fairly straight forward, but a 10-bit monitor is going to be really really expensive.

Monitors vary tremendously in contrast, gamma, color balance, and the ability to adjust them.

The standard response to questions like this is to suggest calibrating your monitor. This is certainly a good thing to do in order to make the most of your monitor, but a poor monitor is still a poor monitor. Calibration allows you to generate an ICC profile for you monitor. In lieu of direct calibration, using a published ICC for you monitor is a good starting point.

So should you upgrade?

Ultimately that's up to you, a new monitor won't be magical but your current monitor leaves much to be desired. A big 4K monitor is much nicer to work with, but be aware it takes substantially more video horsepower to run.

Without a properly calibrated monitor with wide color-space coverage you are basically operating blindly, so for sure you need a better monitor but its not necessarily the resolution.

Start by looked for a monitor with good coverage of sRGB or AdobeRGB. Color-critical monitors can get 100% coverage for those but anywhere over 95% is fine. Try to find a monitor that you can calibrate. Those will often advertise a LUT/3D LUT, the more bits in the LUT, the better. NOTE This is different than calibrating the graphics card which introduces a loss of precision that causes banding and other color artifacts. While you can calibrate your graphics card even for you actual monitor, it will not do much good if color coverage is poor. The calibration process reduces innacuracies but can't make colors not possible with your monitor visible.

Most images are 8-bits-per-channel which corresponds to your 16M colors. This is sufficient for most people. 10-bit is theoretically better since it gives you 1 billion possible colors but support is really limited now, so the difference will likely not be noticeable for a while but getting a 10-bit monitor will reduce the likelihood that you will feel like changing it in the future. High end monitors are very durable and will easily last 10+ years, so consider the amount you want to spend on a monitor as spending for all those years!

Resolution is not that limiting anymore. In fact, it is harder to see detail on a higher resolution monitor because pixels are so small. You'll end up zooming in more than before to compensate. For a long time I was driven by advances in resolution and always upgraded as soon as higher resolution existed but once I got to 4K on a 27" display, discerning details become harder. Probably 32" would have been fine but otherwise, 2560x1600 QHD+ seems like the sweet spot but it may depend on your visual acuity.

Normally I'd say that you've just got GAS and are dying to throw money at something that would be better solved by gaining more knowledge and experience. That's the answer to the vast majority of "Should I spend money on this to improve my photography?" types of questions.

But a 19" 1440x900 monitor in 2021 is pretty weak. I'd say you could definitely benefit a good bit from getting a solid 24" (or larger) FHD (or higher resolution) IPS monitor with near 100% coverage of sRGB.

Things to look for:

• IPS. In plane switching. It makes colors look the same at a wide variety of viewing angles.
• True 8-bit technology, rather than "8-bit" that is actually 6-bit + FRC.
• Near 100% coverage of sRGB at a minimum. Most monitors with around 99% sRGB coverage will also be rated at 72% of the older NTSC color television standard.

Is my monitor inhibiting my post processing?

There's no way to know without more information about your other equipment and workflow.

...not being able to appreciate the fine detail contained in digital files...

Zoom in (pixel peep) if you need to see detail. This would apply to any monitor you purchase because the practical consumer max is only 8mp (4k), but most digital cameras, even phone cameras, easily capture far more than that.

... I may be over-processing...

Buy a colorimeter, and calibrate your monitor. Even if you buy a new monitor, you'd still need to calibrate it.

Some popular colorimeters are i1, colormunki, and spyder. Older models are cheap, especially if they don't come with the original software, which may not work on modern operating systems anyway.

The original software may be downloadable from the manufacturer website. You can also use DisplayCAL instead.

Then use custom white balance and adequate lighting when photographing your subjects. Photograph a calibration target if color accuracy is important.

No, your monitor is fine as long as it is calibrated correctly and it's at the proper viewing angle. If your monitor does not offer the adjustments you need or is dying you should get a new one. However, if it is adjustable and working it is not hindering you. A larger monitor will only make you zoom in more often.

You've got to cover :

• resolution
• bit depth
• color space
• calibration possibilities
• possibly size is also a factor

Better is to adapt to the photos you are editing.

If you're working on pro photography, it is likely that 8bits (16 million colors) and sRGB color space is not enough. Gradations will not be smooth enough. Even Adobe-RGB could not be enough if you are editing iPhones pictures that are now in the new Display-P3 color space, with deep reds.

If you're working exclusively on web pictures, your current display could be enough.