Hey Anton, thanks for your question! 
I think you have several points that point in the right direction, however, here are some of my ideas that may help guide you as well.
In a Bayesian model, each observation—whether it is a daily data point y_t or a lift measurement Δy—contributes a term to the likelihood. The posterior arises from the product of all these likelihood terms and the prior(s). In other words, theres no actual difference between priors and data, they both carry the same weight and multiply in the numerator of Bayes theorem. There’s no discrete “decision” about which part of the data (or which prior) to weight more; it all goes into the same log‐posterior function. The sampling or optimization algorithm (MCMC, variational inference, etc.) explores the parameter space in proportion to the posterior probability (which is prior × likelihood). Whichever parameters jointly give higher posterior density get visited more often by the sampler.
The model does not separately decide “weigh this daily observation more,” “weigh that lift measurement less,” etc. Instead, each piece of data adds a term to the log likelihood. The prior(s) add a term to the log prior. All of these sum up to the log posterior, which is then exponentiated for the posterior density. The acceptance depends on how the log posterior changes. If you move to a region with much higher posterior density, that move is usually accepted; if you move to a region with much lower density, it’s likely rejected. Over many iterations, the chain “spends more time” in regions of high posterior density. Hence the algorithm “pays more attention” to wherever the prior–likelihood combination is largest.
Regarding your first question then: “Does adding one lift_measurement have the same effect as adding one day of data?”. Not necessarily. It is just one more observation in the likelihood, but the model may treat it as more (or less) informative. If you have many daily data points and only one lift measurement, the collective effect of the daily data can outweigh that single new measurement—unless that one measurement is extremely precise and makes the sampler explore a informative region.
“If I have fewer daily data points, does that make the lift_measurement more impactful?”. Not sure more impactful is the word, but potentially yes. If you only have 7 days of data, one lift measurement with moderate or small σ\sigma can push the posterior more than if you had 365 days (i.e., more total daily evidence).
“If I copy the same lift_measurement multiple times, will that make it more aligned with that lift measurement?”. If you repeated the exact same lift measurement multiple times—literally copied that row many times—then from the model’s perspective, you now have multiple identical observations. This is equivalent to telling the model, “We have repeated experiments all measuring the same lift with the same σ\sigma.” That repeated evidence would definitely shift the posterior more than a single instance because the likelihood gets multiplied that many more times. That would risk overstating confidence in that measurement. If that repeated measurement is incompatible with your day-to-day data, the sampler often throws up warnings (divergences, weird posterior shapes) because there is no “comfortable” region of parameter space that fits both your repeated lift claims and the rest of the data.
Remember PyMC its a structural bayesian programming language, we sample a specific data generation process, by consequence any sampler will suffer if you force the exploration around something its not support by your real data generative process (a.k.a your data).
“Decreasing the sigma of the lift_measurement gives it more weight—how to compare that effect to daily observations?”. I don’t have a precise answer for this, it’s hard to compare the effects between one and the other, as mentioned before, the intuition will be that small sigma will make the log-likelihood will be sharply peaked—so it can exert strong influence on the posterior (The sampler may suffer). As mentioned, each additional observation, including new lift measurements, contributes another log-likelihood term in the sum. Using large sigma over the observation it provides only a weak push and can be overshadowed by other data or a strong prior.
I hope some of this sheds some light on exactly what you’re looking for! 
cc: @wdeanHPA @juanitorduz