You're okay, nothing to worry about. Getting lots of soft pulls and Pre-approvals means yare are handling your credit well and you should be pleased. I have 14 credit cards and still have tons of Pre's in my mailbox each week.
Congress provided authority to creditors under the FCRA to make inquiry to the CRAs for a list of consumer names and addresses provided the creditor has established criteria for making them a "firm" offer for credit or insurance.
They do not get the consumer's full credit report, only a list of names and addresses.
Such inquiries are specifically barred under the FCRA from appearing in a consumer's credit report available to others, which is the definition of a "soft pull."
The exclsion from showing on credit reports available to others extends to those who do credit scoring, and thus such inquiries cannot, by statute, be included as part of your credit score.
The credtor hopes that the consumer will, upon receipt of their offer, make an actual application. If the consumer appllies, that is a consumer intitiatted request for credit that then gives them permissible purpose to obtain the consumer's entire credit report. That inquiry may then be shown as a so-called "hard" pull.
I have received three of these pieces of mail; one for express clothing, one for discover, and one for American Express (although this is moreso an invitation to apply).
Keep in mind that preapproved and invited to apply or preselected to apply are very different things.