Nuclear attack subs are normally considered to be strategic platform like aircraft carriers even if they are not carrying nuclear weapon.
Well here's the google AI answer:
A "strategic submarine" is primarily designed to carry and launch long-range ballistic missiles, serving as a key component of a nation's nuclear deterrent, while a "tactical submarine" is focused on attacking other ships and submarines on the battlefield, using torpedoes and other weapons for direct combat operations; essentially, strategic submarines are for long-range nuclear strikes, while tactical submarines are for more localized, immediate attacks.
Here's the Britannica answer:
…new kind of submarine, the strategic submarine. The other is a revolution in antisubmarine warfare, with attack submarines becoming the primary antisubmarine weapons. Attack submarines are armed with torpedoes and, in some cases, with antiship missiles. Strategic submarines may carry similar weapons, but their primary weapons are submarine-launched ballistic missiles…
In the case of submarines, "strategic" has a very specific meaning, and means nothing other than "carries alot of SLBMS". Note that an Ohio SSGN is no longer considered a strategic submarine, but a tactical one, just like any other SSN with VLS tubes.