Can government track VPN traffic if it has control on both ISP and website server?

Do typical VPN providers use the same IP address to receive data from ISP and send data to the destination server (example.com)?

This does not matter much. VPN have a severely limited number of entry and exit points. The protocols used are usually different from normal web traffic (i.e OpenVPN, Wire, IPSec, ... have different communication pattern) and from the perspective of a server one can usually easily find out of the traffic comes from a VPN - this is actually often used to block such traffic when the access should be restricted to specific geographic locations.

If that is the case, can the government identify me, by matching VPN server address and timestamp in ISP log and server log of example.com?

If somebody has access to both the VPN-protected traffic sent using the ISP and to the traffic leaving the VPN then it is likely possible to correlate incoming and outgoing traffic and based on this associate specific server traffic with a specific customer of the ISP.

But likely this is not possible based on the log files of the VPN and server, assuming that the VPN logs contain only information needed for billing. If the VPN logs instead contain a detailed log of all outgoing connections and the associated VPN customer IP address, then these can be correlated with the server log. The VPN customer IP address can then associated by the ISP with a specific ISP customer.

Note that it is likely not possible to identify the client based on a single request. But the more requests are done and the more likely traffic patterns can be associated, even if some "noise" (i.e. small delays, a bit of fake traffic) was added by the VPN.

When you say government, you are implying a certain level of privileged access. Not sure how much of that you are thinking about such as your computer, local ISP, VPN provider, hosting provider for the website;

Here's some variations, assuming that gov always has control over your local ISP (or can request sufficiently detailed logs and traffic captures):

• gov has control over the VPN provider:

can the government identify me(...)?

Yes. They will be able to match your connection to the VPN, look into the VPN logs or traffic and match to the website.

• gov has control over your computer:

can the government identify me(...)?

Yes if they can pull logs from the website owner including session identifiers;

• gov has control over the hosting provider of the website (sufficiently to analyse traffic:

can the government identify me(...)?

Not in a very deterministic way. If they can pull in logs from the website, they could try to match slight peaks of traffic (handful of KBs/MBs) to page hits. But without checking your computer and maybe matching session identifiers, this seems very circumstantial;