Continuous loads - 80%
Your question is all about "continuous loads". That is any load which is likely to be run continuously - including heaters, air conditioners, lighting, and some things you might use serially, like dryers. And of course, Bitcoin miners!
You can only load a circuit to 80% for continuous loads. **
That means on a 15A circuit, you can only load that to 12A (1440 watts) of continuous load, counting all loads on the circuit. I would buy a $20 power monitor (e.g. Kill-a-Watt) and see if that power supply really does draw 1600W; it may draw less.
Whole house (well, 2 half-houses) matters too
Your entire apartment has a 125A breaker, but that's two legs of 120V. Given the 80% rule, each leg can load to 100A only, so 12,000W per leg, or 24,000W total if you balanced it perfectly. That's for all continuous loads in your house, including all the other stuff. That leaves you no margin for non-continuous loads.
This is tougher to monitor, and requires an understanding of which circuits are on which legs. Do not carelessly put 150A of load on one leg, and 50A on the other. Once you learn how your type of panel is laid out, it's fairly obvious which breaker is on which leg. You can also buy a whole-house power monitor, but that requires installation into the panel, as it permanently installs clamp ammeters around your main power feeds.
Talk to your power company!
Ask them about rates which fit your usage. One asker had a totally crazy power plan, where he paid for his highest monthly spike ($6.50/kw), but power was nearly free (0.9 cents per KWH, not a typo). Usually that's a sucker bet, but it's a perfect plan for you. Even if you did nothing to mitigate peaks and ate the extra spike charge, that still totals out to 2 cents/kwh effective. If you do have some power management to back off bitcoin load when other load is peaking, you could tuck it all under the normal peaks and pay the penny rate. Crazy.
So talk to your power company and see what plans they have.
Lastly, if the landlord is paying for this power, clear it with him, or expect big consequences.
** The gory details: the circuit's capacity must be
not less than the noncontinuous load plus 125 percent of the continuous load. NEC 210.19A1, 215.2a1, 215.3.