The short answer is “not much.”
The Court provided no meaningful guidance on whether it had any views on the substance of the allegations made by Texas against Pennsylvania, Georgia, Wisconsin, and Michigan. Nor did it suggest who, if not Texas, might have a basis to assert violations of the “Electors Clause” by state and local officials.
The Order stated that Texas lacked standing, but unlike the circumstances in lower court decisions, it is not necessary for the Supreme Court to provide a reason for its conclusion in this regard. Lower courts do so because their decision is subject to review and appeal to a higher court by the litigants. Since that is not possible with a decision from the Supreme Court, there is no need for them to explain the “why” behind their decision — and they did not.