Add External DAC or Upgrade to a New Streamer / DAC?

With USB connection DAC uses its own free running clock and requests data from streamer when it needs a new portion. USB connection is asynchronous and does not carry any clock information - only request from receiver (DAC) and response from sender (streamer). In that case jitter is only limited by the quality of DAC internal clock.

Other type of connections are synchronous and thus all devices should be slaves of the same clock source. This can be DAC internal clock (propagated to streamer), or DAC  is also a slave to some external clock source. But in that latter case jitter is limited by the quality of DAC circuit that synchronizes local clock with external master.

If clock distribution is not possible, then ASRC in DAC is the only way to minimize jitter, but ASRC may add its own distortion.

Streamer is a computer and needs to be evaluated as such - mostly by features available in software. DAC is evaluated on quality of a single function it does - digital to analog conversion. Software and features are changing much more often, that is why it makes more sense to separate streamer and DAC. But with that separation you should choose streamer with USB output and DAC with USB input. If there is not USB and you have to use AES/SPDIF/TOSLINK, then to deliver bits perfectly from streamer to DAC you need to choose DAC that has master clock OUTPUT and streamer with master clock INPUT. This is the only solution (other than USB) to make streamer slave to DAC clock.

I2S is equivalent of SPDIF from clocking perspective and only appropriate when DAC supplies clock signal to streamer.

The only audio transport for Ethernet is AES67/Dante. There are not many DACs supporting it on the market and even less number of streamers. In Dante based networks clock distribution is even bigger issue and today likely requires ASRC feature inside DAC to minimize jitter.