Since you have returned to India for long-term stay, your case should now be examined as a Resident under FEMA. In such a situation, the NRE account should generally be redesignated, and the FCNR proceeds on maturity should ideally be transferred to an RFC Account or Resident Account, as applicable.
Accordingly, if you now wish to make fresh investment in overseas USD funds or GIFT City products, the correct and safer route is generally through your RFC / Resident banking channel, and LRS would ordinarily apply if you are treated as a Resident Individual under FEMA.
Therefore, direct transfer from NRE account to overseas / AMC account is generally not the proper route. Even if the bank technically permits such transfer, FEMA / LRS compliance will still apply.
In our view, you should first regularise the funds through the RFC Account and then make the investment through the proper banking channel after checking your exact FEMA residential status.
For a more detailed opinion based on your facts, bank status, and proposed investment structure, kindly book a phone consultation.