What has me worried is that my 3060ti uses 1 8pin connector, a colleague has a 3060 and it uses 2 8pins. Does this matter?
No, it shouldn't so long as you connect all the connectors from the PSU to the GPU(among other things) to make sure that they receive the power they need in order to operate optimally. There are thumb rules with PSU's. One of them is if the PSU you have doesn't have the necessary connectors for your devices, you either have the wrong PSU for the job or the wrong components(without the PSU) for the job.
Not all AIB designs are the same...heck they don't use the same power regulators. They (can)use the same GPU chips on the board but the board design can be reengineered to meet a specific design objective/price point/demographic. Case in point, mini version discrete graphics cards have limited space and connectors but don't have limited power output from GPU's end.
Your colleague has the same GPU(and SKU) as you?
As for the 12pin connector mentioned, you referring to the EPS connectors at the top of the board near the CPU socket? If so, they are never counted cumulatively, they are calculated as 4pin or 8pin. So for your instance it's 1x4pin EPS and a 1x8pin EPS connector.