Thrawn was a Grand Admiral, but he was dissatisfied with the Empire's system and reality.
Maintaining the system and centralization was common sense in the Empire at the time, and he could not reform it alone. He kept silent.
This means that he could analyze the Empire objectively. As an admiral, he had access to many secrets and reports, so he was given time to devise the next generation of doctrine. This was later to become the First Order Plan.
Thrawn's idea was an experimental empire in a sense. He didn't know if it would be implemented, but it was unique and valuable. It would later be proven to be correct.
He kept it a secret from the Emperor. He would never have advised the Emperor.
Because denying centralization would be like asking the Emperor to give up his power.
In simple terms, it was a criticism of the Empire at the time. As an admiral of the Empire, he must not interfere with maintaining the system.
Thus, the First Order Plan, which he devised as an admiral, was incubated for a long time. Thrawn himself never thought that it would actually be implemented later.
After the death of the Emperor, you can put your ideas into action. Thrawn was recommended to become the second Emperor.
But he refused to become Emperor himself. He rejected the idea of a dictator.
This is an important point in the First Order plan.
The Emperor had been planning a plan in case he died, but he didn't know about Thrawn.
Thrawn was not the kind of person who would aim for the position of Emperor, so he trusted him.
He probably imagined how Thrawn would think if he told him the truth about the Clone Wars and the true identity of Lord Vader.
The death of the Emperor proved that Thrawn's ideas were correct. It is the downside of centralization. A system that relies on the Emperor is fragile and dangerous.
A strong Empire will collapse all at once. The First Order plan was a move that was carried out under the surface in the midst of that chaos.
Thrawn lamented the death of the Emperor. In fact, it was a favorable development.