MacBook pro 13" A1502 Early 2015 Retina Battery issues

Unfortunately any battery or power related issues will usually cause a Retina model Mac to run slow...the hardware issue must be addressed...whatever that hardware issue is.

Without a good battery, there is no good way of testing the laptop. Even Apple and an AASP will not be able to properly test the laptop until another battery is installed.

At best, we can look for possible software issues. To do this, run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper. If we can confirm a contributing software issue, then maybe Apple or the AASP can re-examine the laptop again to see whether the battery will be sufficient to resolve the problems.

I don't see anything in the report which would normally cause a problem except for One Drive and Google Chrome. Google Chrome is known to take up a lot of memory & CPU cycles while One Drive can slow the system down due to how it accesses the drive to sync files to the cloud. Otherwise, I don't see a problem, but you are using a couple apps which I've never seen such as the RunCat app.

You can try running Disk Utility First Aid on the hidden Container. Within Disk Utility click "View" and select "Show All Devices" so that the hidden Container appears on the left pane of Disk Utility. Even if First Aid says everything is "Ok", click "Show Details" and scroll back through the report to see if any unfixed errors are listed. If there are any unfixed errors listed, then try running First Aid from Internet Recovery Mode (Command + Option + R), otherwise you will need to erase the whole physical SSD followed by reinstalling macOS & restoring from a backup. Erasing the drive will destroy all data on the drive.

Otherwise unfortunately without a good battery, there is no to know how a Retina model laptop is performing since a missing battery will cause performance issues (any power issue can cause a performance issue).

OWC is the best option for a third party Lithium-ion Battery and they have authorized resellers for other regions.

The next best option is iFixIt, but I believe they are more expensive.

FYI, No report was was posted.