In the given question, we need to evaluate the correctness of two statements regarding recent actions by the Employees' Provident Fund Organization (EPFO) and select the correct option based on these statements. Let us analyze each statement:

1. Statement 1: "EPFO has enhanced member services by increasing the auto-settlement limit for advance claims from the existing ₹ 1 lakh to ₹ 3 lakh."
   • This statement refers to a specific operational improvement in the auto-settlement mechanism used by EPFO for advance claims.
   • As of the latest updates, no official announcement by EPFO supports this change in the auto-settlement limit from ₹ 1 lakh to ₹ 3 lakh. Therefore, this statement is incorrect.
2. Statement 2: "EPFO first introduced auto-settlement of advance claims during the COVID-19 pandemic."
   • This statement examines the timeline of EPFO's implementation of auto-settlement features.
   • During the COVID-19 pandemic, to provide financial relief, EPFO did introduce various measures including auto-settlement facilities to expedite advance claims.
   • Hence, this statement is correct.

Based on the analysis above, the correct answer is provided by the code corresponding to statement 2 only. Therefore, the correct answer is:

2 only

Conclusion: Reviewing current updates and official announcements, statement 2 accurately reflects EPFO's past actions during the COVID-19 pandemic, whereas statement 1 lacks evidential backing of recent enhancement in the auto-settlement amount. Hence, only the second statement is correct.