What's the term for "government worker"?

They are public sector employees (as opposed to private sector employees)

The public sector is the part of the economy concerned with providing various governmental services. The composition of the public sector varies by country, but in most countries the public sector includes such services as the military, police, infrastructure (public roads, bridges, tunnels, water supply, sewers, electrical grids, telecommunications, etc.), public transit, public education, along with health care and those working for the government itself, such as elected officials. The public sector might provide services that a non-payer cannot be excluded from (such as street lighting), services which benefit all of society rather than just the individual who uses the service.

Businesses and organizations that are not part of the public sector are part of the private sector. The private sector is composed of the business sector, which is intended to earn a profit for the owners of the enterprise, and the voluntary sector, which includes charitable organisations.

— Wikipedia

In English, there is no single umbrella term systematically used for workers employed by the government (unlike the word "fonctionnaire" in French or the terms "funcionario" and "funcionario público" in Spanish).

The various terms that may be used are:

• public/civil servant,
• public official,
• senior/minor [government] official,
• state employee,
• government/public worker/employee,
• functionary.

But I am surely forgetting some other expressions.

Your feelings about the word 'official' are well founded; it has similar implications in American English.

The term I would use is 'civil servant' or 'public servant'. This could be used for anyone from a postal worker to the president, though there are some jobs I am not used to it being associated with, military members being one class. According to Wikipedia these terms only officially refer to national government employees, but I believe colloquial use is much broader.

Here's some info in the context of India :

In India , a person drawing his salary directly from taxpayer's money is called Public Servant.

The word Civil Servant on the other hand carries a Raj era legacy when the country was governed by the Indian Civil Services. Even though the ICS is defunct now, the term Civil Services is reserved for mid to high level bureaucrats and other government officials. For instance, the government conducts civil services exams for recruitment of mid to high level officials and Staff Selection examinations for lower levels in its hierarchy.

So Public Servant is the all-encompassing word for anyone working for the government. A legal definition of the word is here

The word Public Sector in India has a special meaning. It refers only to various business organisations run by government due to its soft socialist nature. These include a number of petroleum companies , mining companies , banks etc. Their day to day operation is not supposed to be funded by government and in most cases they compete directly with their private counterparts and pay dividends to government. A huge multitude of people working in them are called Public Sector Units (PSU) employees