8/30/2018: Edited to address OP's follow-up question of whether section 250.512 of the Landlord and Tenant Act precludes recovery of security deposit (see comments)
After analyzing the statute you found, Pennsylvania courts have still held that a tenant's failure to provide a new address does not preclude recovery of the security deposit.
See Adamsky v. Picknick, 412 Pa.Super.Ct. 544, 549 (1992):
we find the lack of notice argument is tenuous at best since
appellant's reason for withholding the deposit was not because he did
not have appellees' new address, rather, he withheld it because he
maintained there were damages for which he should be compensated.
That conclusion is squarely applicable to your situation. The landlord's only pretext for withholding your deposit is his inaccurate statement that "you did not provide proper notice of moving out", and for that matter he refers to nothing else than the rental agreement. The rental agreement nowhere requires you to provide your new address.
One decision that does not constitute legal precedent but still might help persuading Small Claims court in your situation is Back v. Taylor, 19 D. & C. 3d 606, 609 (1980). After citing section 250.512(e) of the Landlord and Tenant Act, the court states:
That section sets forth certain guidelines as to when tenants can
obtain double recovery. Defendants have only sought recovery of the
deposit and therefore, the above cited section does not apply.
(emphasis in original)
Unless you were pursuing double recovery, it would be very questionable --to say the least-- why a [Small Claims] court should decide your dispute any differently than in Back.
Another non-precedential decision analyzing the same statute is Shoemaker v. Henry, 35 D. & C. 206, 209 (1984). Also in the context of double damages, the court stated:
We cannot believe the only purpose [to require a tenant to provide his
new address] was a negative one, that is, to cancel a right to double
damages for failure to comply. A more rational explanation is that its
purpose was to provide a landlord with an address to which the damage
list could be sent.
(brackets added)
The statute apparently was enacted well before the prevalence of electronic communications. If your landlord has any way to send you a "damage list" (as it seems to be the case insofar as he replied to your text), then the rationale in Shoemaker should apply in your situation. If you are not even pursuing double recovery, then it would be unavailing for the landlord to cling to the language in item (e) of that statute.
Therefore, you are definitely entitled to your deposit even if you did not provide to the landlord a new address. It is up to you whether you want to go for double damages, in which case the decision in Shoemaker might or might not be persuasive in Small Claims court. Beyond that, the Adamsky opinion constitutes legal precedent which favors your position.