Is it normal for spam to spike right after joining a store loyalty program or is that a security red flag?

I signed up for a retail loyalty program last week and almost immediately started seeing an increase in spam emails and even a couple of strange texts. I am trying to figure out if this is just bad timing or if these loyalty programs share customer data far more aggressively than people assume.

I know some stores use third party marketing platforms and data partners, but I did not expect the jump to happen this quickly. I unsubscribed from their emails, but that only stops one channel and it clearly did not prevent the spam texts.
For anyone here who works in cybersecurity or deals with user privacy, is this a known pattern. Do loyalty programs usually hand off your info to external partners, or could this be a sign that my email or phone number was already floating around in a broker database and the timing is just making it look connected.
If this is something that happens often, what is the safest way to protect email and phone details during signups. I am starting to think I should avoid using my real contact info for basic retail accounts, but I do not know what the standard privacy friendly approach is. I just want to prevent my details from being passed around again.