Although it doesn’t answer the interpretation question between Model 1 and Model 2, I did stumble across this thread by @Solomon, which provides input into how this interaction could be specified: How to properly compare interacting levels - #6 by Solomon
For my example this would be outlined as below; it appears to be equivalent to Model 1.
outcome ~ 0 + a + b + c,
a ~ 0 + group,
b ~ 0 + covar,
c ~ (0 + group) : (0 + covar)