It might be helpful to have sleep tracking to have a better idea of what you need.

There's hardware like https://dreem.com/en/product that promises to help people sleep better.

General tips for better sleep are about avoiding blue light right before bed. I sat my f.lux so red that green and black became the same color. In addition I have Philips Hue lights that dim red.

Cool down the room when you are sleeping.

Make the room in which you are sleeping pitch black.

Don't eat anything 2 hours before going to bed.

• Get more sleep at night.
  • Take melatonin at the appropriate time and dose. It's cheap and legal in the U.S., but most products have way too much. https://slatestarcodex.com/2018/07/10/melatonin-much-more-than-you-wanted-to-know/ most insomnia drugs are not much more effective than this.
  • Avoid light at night, especially blue light. Light inhibits natural melatonin production, which interferes with you circadian rhythms.
    • If you can't darken your room completely, you can use a sleep mask instead. Get the kind with cups (like opaque swim goggles) instead of the kind that puts pressure on your eyes.
    • Use f.lux on your personal devices to reduce blue light after sunset or use one of the similar built-in features of your OS. Windows 10 has the new "Night Light" setting, macOS and iOS have "night shift" mode. Newer Samsung phones have a "blue light filter" setting. These options vary in quality and may have configurable intensity. More intense is more effective and it's surprising how much you get used to it.
  • Falling asleep is a common failure mode of certain types of meditation practice. You can use this to your advantage when suffering from insomnia in bed. Even beginners fail to meditate this way accidentally, so it's not particularly difficult to do on purpose. Focus your attention on the sensation of breathing or on the ringing in your ears. When you notice you are lost in thought, refocus your attention. But when you notice the dreaming arise without directed effort, dive in and let them take you. It works for me anyway. If not, at least you got your meditation in today.
• Take naps. Even 20 minutes dramatically improves performance when sleep deprived.
  • Try the sleep mask when napping.
  • Try the meditation techniques for naps too.
• Track your sleep quality.
  • You can get smartphone apps that purport to do this using the phone's sensors. Some fitness trackers or smartwatches also have this function built in or available as an app. Accuracy varies.
  • You may have sleep apnea. Talk to your doctor about doing a sleep study to diagnose possible issues and treatments. Some people do much better on a CPAP, but there are many other treatment options.
• Avoid eating late at night. This can cause indigestion, which can keep you awake.
  • if you suffer from heartburn, sleep on your left side to contain it better, because your esophagus attaches to your stomach on the right side (unless you're one of those rare people with backwards internal organs).
• Exercise regularly. I'm not sure why this helps, but it seems to. Perhaps mental fatigue doesn't always line up with physical fatigue unless you actually make some effort physically during the day.

Methods I've personally found useful for improving productivity when temporarily my cognitive ability or conscientiousness is lowered, not necessarily due to sleep deprivation:

• Selecting from my TODO list tasks that are either non-demanding, or very exciting
• Sitting next to a big window and spending a lot of time people-watching. I don't understand why it worked, but I noticed it would put me in a rhythm where I would make slow but consistent progress with my work.
• When a lot of mental energy needs to be mustered (and so the above two methods are not an option), cut out all the stimulation: put away my phone; close all the non-relevant web browser tabs; put on noise-cancelling headphones with pink noise playing; go to a separate room and/or use big objects to restrict my field of vision to nothing but my workstation. Also, make sure that I won't be disturbed for the next couple hours at least: prepare a glass of water, go to the toilet, make sure my co-workers understand this "do not disturb" mode.

You seem to assume that your lowered ability is caused by sleep deprivation. Is that an assumption? If so, I would encourage you to track your sleep quality and your cognitive performance and see if they really correlate, if you can think of a way to do it.

My fully subjective impression is that my insomnia never impacted my cognitive performance. I used to stress about it impacting my bodybuilding. Then I started believing that the impact of my sleep deprivation is minimal, if any, and that new belief probably helped me improve quality of my sleep.

An off-label use of fluoxetine (Prozac) is that it can caused prolonged sleep, possibly by reducing anxiety in ways that make it easier to stay asleep longer but specific mechanism of action is unknown. Worked well for me in treating narcolepsy-related sleep depravation, i.e allowed me to stay asleep 10 hours a night so I got enough sleep to avoid sleep attacks during the day. I'm no longer on it and still able to get enough sleep; my theory there is that regular meditation replaced the need for a drug to produce the same effect, allowing me to stay asleep longer.