IANAL either, but from what I've read before the courts treat searches of your home with extra care under the 4th Amendment. At least one circuit has pushed back on applying private search cases to residences, and that was for a hotel room[0]:
> Unlike the package in Jacobsen, however, which "contained nothing but contraband," Allen's motel room was a temporary abode containing personal possessions. Allen had a legitimate and significant privacy interest in the contents of his motel room, and this privacy interest was not breached in its entirety merely because the motel manager viewed some of those contents. Jacobsen, which measured the scope of a private search of a mail package, the entire contents of which were obvious, is distinguishable on its facts; this Court is unwilling to extend the holding in Jacobsen to cases involving private searches of residences.
So under your hypothetical, I'd expect the police would be able to test "your drugs" that they confiscated from the thief, and use any findings to apply for a warrant for a search of your house, but any search without a warrant would be illegal.
> Unlike the package in Jacobsen, however, which "contained nothing but contraband," Allen's motel room was a temporary abode containing personal possessions. Allen had a legitimate and significant privacy interest in the contents of his motel room, and this privacy interest was not breached in its entirety merely because the motel manager viewed some of those contents. Jacobsen, which measured the scope of a private search of a mail package, the entire contents of which were obvious, is distinguishable on its facts; this Court is unwilling to extend the holding in Jacobsen to cases involving private searches of residences.
So under your hypothetical, I'd expect the police would be able to test "your drugs" that they confiscated from the thief, and use any findings to apply for a warrant for a search of your house, but any search without a warrant would be illegal.
[0] https://casetext.com/case/us-v-allen-167