Inspectors also found staff shortages were still a concern, despite some recent recruitment.
Improvements had been made, included introducing a 24/7 urgent helpline, but the service still did not always assess emergency referrals within four hours, in line with national standards, it added.
Feedback was “mostly positive” about staff attitudes and behaviours, and most people felt safe, understood and involved, the CQC found.
At community services for adults, which had improved from “requires improvement”, people described staff as caring, respectful and inclusive.
People felt safe and were confident to raise concerns, but the CQC also found staff did not always share care plans or risk management plans.
NSFT Crisis Campaign, which seeks to improve the service, said in a statement it was “the first time in a long time the trust is not going backwards”, but said this was down to “scaffolding” from NHS England and the CQC.
“The campaign still has great worries about the scale of change that needs to happen at the trust for it to at least operate as a safe and effective service,” it added.
Ms Donovan said the reports were testament to the dedication of its hardworking staff, who had “focussed relentlessly on improvements”.
“We are proud that these reports have acknowledged significant improvements we have made,” she added.
“However, we also recognise we have more to do to ensure we are consistently providing safer, kinder and better services to everyone who needs our support.”