One- vs two-sided credible interval for Poisson process with all zero counts In a related question, I asked about a confidence interval for the estimate of the mean of 50 observations of a Poisson random variable, for which all 50 observations had a count of zero. In the comments to an answer to that question by whuber, it was pointed out that you shouldn't use a one-sided confidence interval just because you have all zero counts. If you used a two-sided interval in situations where you observed non-zero counts and one-sided intervals when you observed all zero counts, your confidence intervals would no longer have their nominal level of coverage.
In that question a simulation of coverage convinced my that that was a bad strategy.
My question here is how would a Bayesian argue one way or the other for one- vs two-sided credible intervals for the same situation with all zero counts.
Consider a prior distribution of $gamma(1, 0)$, with a Poisson likelihood, that results in a posterior distribution of $gamma(1, 50)$, for data consisting of 50 observations of zero counts.
How would you argue against using a one-sided credible interval?
 A: Interesting philosophical issues arise with very small Poisson rates. Also
with the choosing of appropriate prior distributions for Bayesian analysis
of low rates.
Hypthetical particle. Suppose I'm looking for evidence of a theoretically predicted, but never
observed G-particle. After 50 runs of my particle collider, I have seen
no traces of the kind G-particles should make. So in 50 runs I have seen
no evidence that G-particles exist.
According to your prior, I have two possible 95% credible intervals:
two-sided $(0.0005, 0.0738)$ and one-sided $[0, 0.0600)$ or "rate below 0.06."
qgamma(c(.025,.975),1,50)
[1] 0.0005063562 0.0737775891
qgamma(.95,1,50)
[1] 0.05991465

On what grounds would you defend the two-sided interval with its lower bound
$0.0005?$ Certainly, I have no empirical evidence for existence of G-particles,
so that implied possibility of a non-zero rate relies altogether on (perhaps unintended) 'information' from
my "noninformative" prior.

You ask, "How would you argue against using a one-sided credible interval?"
In this scenario, I would not make such an argument. But as always, you might find someone with a different opinion.

Rare particle. How is it different if I am trying to figure out if my collider is capable
of observing H-particles, which are known to exist, but to be very rare?
Then I might choose a prior that focuses on the characteristics of my collider.
The lower limit of a two-sided credible interval might be interpreted
as a lower limit of my ability to detect H-particles.
