MacBook Pro shuts down after boot up — Battery Problem?

Hello guys,

I am currently using a MacBook Pro (13-inch, 2017, Two Thunderbolt 3 ports) that I purchased in January 2018. This is a recent problem.

I noticed that upon booting up my MacBook Pro, either from Sleep Mode or Power Off, if the MacBook Pro was unplugged, the boot up process will reach the desktop, load up a few apps then shut down again. If I pressed the Power button, the MacBook Pro will tell me that it was low on power and needed to be charged. This despite the fact that there's clearly more than enough battery life left (sometimes more than 80%).

Here's the strangest thing: if I follow the instructions, plug the computer to the charger, the MacBook Pro will return to the desktop (skipping boot up this time). And if I unplug the charger at this point, the MacBook Pro will operate as per normal.

What's going on? Is this a battery issue? Should this happen to a two-year-old MacBook Pro? Is it worth replacing the battery? I have tried resetting SMC settings to no avail.

Here are a few more specifications about my MacBook Pro:

Operating System: macOS Catalina 10.15.5

Processor: 2.3 GHz Dual-Core Intel Core i5

Battery Cycle Count (as per System Information): 267

Battery Condition (as per System Information): Service Recommended