In a nutshell, yes.
Your MacBook Pro battery has a life expectancy at or around 1000 cycles. It's not uncommon for batteries to exceed or fall short of this number; it's just an estimation of how long it can last. You can refer to Determine battery cycle count for Mac notebooks on Apple's website for more info.
It seems you've had a good run overall and extracted most, if not all of the value out of it. It's time to replace it.
Your options are to have the battery replaced or to only use it while connected to an AC power source. There are many 3rd party battery options available for purchase, so if you're still happy with your MBP then that's your best option. If not, then it's time to upgrade.
If you do decide to replace the battery, then I would ensure that you purchase a battery from a reputable online store dealing with Apple products.
For example, the following are some well-regarded sites:
By buying from a reputable store you'll be sure to get a battery fit for purpose, regardless of manufacturer. Being reputable means they're only going to sell something that works and they'll stand behind the product they sell, regardless of the brand.