A renter's policy is ridiculously inexpensive for what you get. Because it only covers liability and personal property, and not the full breadth of coverage a homeowner's policy would have, it's easy to get a really comprehensive policy for less than ~$15 a month. I've only had to use my renter's policy once after a break in, and the payout for personal property coverage was more than my entire decade worth of premiums[2]. Especially if you're a techie, electronics/computing stuff[3] really starts to add up if you take a look at all the little gadgets and computers and home office[4] style stuff you have around.
[1] It basically sets it up so that your landlord gets notified of any policy changes (non-renewal, cancelations, limit changes, etc) and can know for sure that you're continually insured, and don't let the policy lapse after you've shown your proof of insurance at lease signing.
[2] Paying a few extra bucks for "replacement cost" coverage vs. "market value" coverage is well worth it. It's the difference between "here's $100 for your 5 year old MacBook Pro" and "here's $1000 to cover the replacement cost for another entry level MacBook Pro".
[3] If you have personal property replacement, you'll generally have per-category limits. If you don't explicitly request a rider for it, your e.g. $20k personal property replacement coverage may cap out electronics at $1k.
[4] If you have company-owned equipment at your house, your personal renter's policy would likely not cover it. If you work for yourself from home, your "for work" equipment is probably not technically covered under a standard renter's insurance policy, so you may want to explicitly clarify if you need a separate policy with your insurance company if you don't want to chance a claim with it getting denied.