From @jyu00 "the quasi probabilities is just counts / shots... but I don't remember the v1 syntax so I'll need to play with it. "

The old output format was a dictionary of with bitstring (in int) as the key and quasi-probabilities as the value for each circuit, e.g. [{0: 0.4589879389380925, 1: 0.5410120610619075}]. The new format has the same key (but as string) and counts as the value. To convert the new format to the old, one can do:

v2_result = sampler_v2_job.result()
v1_format = []
for pub_result in v2_result:
    counts = pub_result.data.meas.get_counts()
    v1_format.append( {int(key, 2): val/shots for key, val in counts.items()} )

And v1_format here is the same result in the v1 format. Note that shots is the number of shots selected per this rule.