According to GSM arena the Google Pixel 3a has an USB 2.0 type-C connector.
Note that the USB transfer speed is independent of the used USB connector type.
Therefore USB 3.0 is not supported by the Pixel 3a - you can only use USB 2.0 connections for data transfer.
The cable you describe is a standard USB converter cable (USB-A to C).
A lot of manufacturer ship such a cable together with a new phone.
You can use it to establish a USB 2.0 (and may be 3.0 if the device supports this) connection between your computer and your phone.
Like any USB cable it is agnostic to the data it transmits, therefore ADB and MTP (file ...
Google store doesn't sell this adapter in India but links to retailers whose product description shows it has a DAC chip and therefore is active similar to this. Note that this works on Pixel 2 and Google Support for Pixel 2 clearly mentions it has a DAC and is active.