Why didn't Mueller have to do this?
Kenneth Star was an Independent Counsel, as you said. However, the law which created that provision expired in 1999. Mueller is a Special Counsel, which performs much the same purpose, but is authorized by Justice Department regulations rather than Congressional law.
Thus there is no legal requirement for Mueller to submit a report to Congress, so he didn't do so.
As Bobson correctly notes, the legislation for the Independent Counsel has lapsed; the new Special Counsel regulations which replace it, 28 CFR 600, set up an indirect reporting. By 28 CFR 600.8(c)
(c)Closing documentation. At the conclusion of the Special Counsel's work, he or she shall provide the Attorney General with a confidential report explaining the prosecution or declination decisions reached by the Special Counsel.
And by 28 CFR 600.9(a)(3)
(a) The Attorney General will notify the Chairman and Ranking Minority Member of the Judiciary Committees of each House of Congress, with an explanation for each action -
(1) Upon appointing a Special Counsel;
(2) Upon removing any Special Counsel; and
(3) Upon conclusion of the Special Counsels investigation, including, to the extent consistent with applicable law, a description and explanation of instances (if any) in which the Attorney General concluded that a proposed action by a Special Counsel was so inappropriate or unwarranted under established Departmental practices that it should not be pursued.
Interestingly, there are few strict reporting requirements for the AG on this: he only has to explain to Congress if he overruled (or dismissed) the Special Counsel. He is not even required to send a summary of the Special Counsel's final report to Congress.
Furthermore 28 CFR 600.9(c) give the AG wide discretionary powers as what to disclose to the public from all that
(c) The Attorney General may determine that public release of these reports would be in the public interest, to the extent that release would comply with applicable legal restrictions. All other releases of information by any Department of Justice employee, including the Special Counsel and staff, concerning matters handled by Special Counsels shall be governed by the generally applicable Departmental guidelines concerning public comment with respect to any criminal investigation, and relevant law.
Even under the old legislation, Mueller might not have had to report anything directly to Congress... because the reporting was predicated on finding impeachable offenses. Starr said:
As the investigation into the President's actions with respect to Ms. Lewinsky and the Jones litigation progressed, it became apparent that there was a significant body of substantial and credible information that met the Section 595(c) threshold. As that phase of the investigation neared completion, it also became apparent that a delay of this Referral until the evidence from all phases of the investigation had been evaluated would be unwise. Although Section 595(c) does not specify when information must be submitted, its text strongly suggests that information of this type belongs in the hands of Congress as soon as the Independent Counsel determines that the information is reliable and substantially complete.
Since the Mueller report to the DOJ doesn't indicate evidence for impeachable offenses (according to the DOJ-released conclusions), Mueller would have probably concluded he doesn't have anything that needs reporting directly to Congress, even under the old law.