Suppose we know that compound X is a selective agonist of receptor Y, meaning that it binds only this receptor Y and no other. But how do we know this that it doesn't bind some another receptor? I suppose that screening for the binding strength of a given ligand to all known receptors would be very tedious and not feasible.
Unfortunately, it's really hard in the general sense. Even for FDA-approved drugs with well-characterized mechanisms of action, the binding profiles are incomplete.
For GPCRs, it's you can run your compound(s) against a full panel of many GPCRs. For example, the PDSP (Roth Lab) can test for binding against multiple GPRCs using radioligand binding assays. See: https://pubmed.ncbi.nlm.nih.gov/23235874/, Figure 2 in particular. Most receptor binding assays are competitive, meaning they detect the displacement of known ligands. This is inherently limited because your compound could bind to a different site -- even a novel site.
You'll notice that in Figure 2, the GABA A receptor was conspicuously missing. One of the reasons is that binding is subunit-specific, which is another complication -- many receptors are oligomers, and it's often hard to prepare them for the assays.
For many well-known enzymes, there are specific activity assays available. These measure the level of a reaction product (often by fluoresence). This of course doesn't rule out binding without activity, and these assays are not available for all enzymes.
Another class of assays measure changes in potential across a membrane. For example, the FLIPR assay for GABA A receptors (https://pubmed.ncbi.nlm.nih.gov/31127604/). These tend to be very time-intensive and expensive, they're limited in the number of receptors, and of course they can't detect binding without activity.
As a last resort, you can use pull-down assays. One of the popular methods is immunoprecipitation (IP). You make an antibody that's selective for your compound and use to cross-link to any protein your compound might be binding to. Then these proteins get pulled out with your compound. These are generally very time-intensive and expensive, and they can need a lot of tweaking. And, of course, they won't detect all proteins your compound might bind to.
It's currently impossible to show that a compound is completely selective. To show that it's "likely" to be very selective, you can expect to invest a year or more for one compound.
But! To take a first stab, you can check out commercial assays offered by Eurofin (ex https://www.eurofinsdiscoveryservices.com/cms/cms-content/services/in-vitro-assays/gpcrs/binding/). They have a GPCR panel and a number of activity assays. Unfortunately their services are quite expensive.