What is an adjective that means constant with a negative connotation?

Incessant is almost always used negatively. Relentless is also really good to make something feel overwhelming, as long as the context indicates a bad situation.

degrading, demoralizing, disintegrating and destroying

Interminable:

[Merriam-Webster]
: having or seeming to have no end
especially : wearisomely protracted
// an interminable sermon

// And yet until last month, many here saw the rise of the cartel as an internal matter for the parties in an interminable drug war. — Kevin Sieff, Washington Post, "Mexico’s Jalisco New Generation Cartel blazes a bloody trail in rise to power," 10 July 2020

// Who’s telling them to maintain a safe distance from each other while standing in an interminable line? — Kevin Sherrington, Dallas News, "Is moving football to the spring really such a bad idea? Like it or not, it’s time to consider the option," 5 July 2020

It could be used in the context of the question in the following way:

The atmosphere of attention, suspicion, and micromanagement was interminable.

You could say he felt dogged by his employers. As an adjective, dogged, as in dogged persistence, dogged pursuit.

From https://www.merriam-webster.com/dictionary/dogged

Definition of dog (Entry 3 of 4) transitive verb

1a : to hunt, track, or follow like a hound

dogged her every move

b : to worry as if by pursuit with dogs : PLAGUE

dogged by his past failures

c : to bother or pester persistently

dogged him about his grades

Perhaps your character feels persecuted? From M-W:

persecute: to annoy with persistent or urgent approaches (such as attacks, pleas, or importunities)

And from under Choosing the right synonym for persecute:

Persecute implies a relentless and unremitting subjection to annoyance or suffering.

Your context:

The character is lamenting the fact that his employers are watching him in a suffocating way and restricting his freedom, i.e., he is being or feels he is being persecuted.