To fit a model with random slopes but without randomerandom intercepts you would use:
glmmTMB(weight_t ~ (0 + t_days | scale_id), data = long, family = gaussian) I haven't checked that glmmTMB supports such a model, but I would assume that it does, but that it how you would do it in lme4
Yes, it would seem that the model with correlated random slopes and intercetps is too complex. This makes sense if the random intercept variance is close to zero, as it would appear from your final model, since the software would be trying to estimate a correlation close to zero and this sometimes does pose problems.
I think it is OK to exclude the random intercepts if you have good reason to believe that there should be no initial variation in measurements accrossacross snakes. Certainly that is what the models are telling you. Sometimes this happens when an analystsanalyst mistakenly adjusts the data to make all the initial measurements the same, which is a big mistake, so as long as you didn't do this, and all the initial measurements really were the same, then you should be good.
Edit: You mentioned in the comment to my answer that this is a model of growth in weight over time. In that case you need to include t_days as a fixed effect, otherwise the model will be severely distorted because random effects are assumed to be normally distributed around zero - and it seems unlikely that you will have nebativenegative growth. So I would go back to this mode:
weight_t ~ t_days + (t_days | scale_id) and proceed from there.
Also as mentioned, you might consider centering time at zero, and incorporating nonlinear growth.