When you want to call a company, you often have to wait and be patient oin a queue.

There are often AI which tells you your number in the queue.

or "there is often AI which tells"

If AI is being used as a singular noun, then the verbs would be is/tells

if plural, then are/tell

But when you're finished ing the queue, you're talking to a real person.

or "when you're done waiting"

But in athe near future, people could be replaced by AI.

more common to say "the future"

A president of thea call centre workers said in a podcast that she is worried about that.

the president is of the organization, rather than the people.

for example: the president of Timbuktu instead of "the president of people in Timbuktu" or "the president of the bank" instead of "the president of bank workers"

Indeed, AI is really a threat for call's centre workers.

But she thinks that an AI can't replace a real person because people are empathetic and, while AI can't be empathetic because it doesn't have any consciousness.

if you have been using AI without "an" up to this point, it might better to keep it consistent throughout

also the comma plus while helps break up the long sentence

you could also consider:

"But she thinks that AI can't replace a real person because people are empathic and (or comma plus while) AI doesn't have any consciousness.

She also said that the purpose of the call's centre workers consists byof pacifying the callers who are often angry and can shout down the phone.

usually consist is followed by "of" followed by the -ing form of the verb

Please tell me how you found my eEnglish!

When you want to call a company, you often have to wait and patient on a queuein a queue patiently.

Indeed, AI is a really a threat for callto the call center's workers.

But she thinkHowever, she believes that an AI can't replace a real person because people are empathetic and AI can't because, whereas AI lacks this quality, as it doesn't have anypossess consciousness.

"However" is a good alternative for "but".
"Whereas" is the correct transition here because you are contrasting with your first sentence.
"Have" is grammatically correct here; however, "possess" is more commonly used to describe personal qualities.

When you want to call a company, you often have to wait and patient oly in a queue.

You have to wait only when you call a company, not when you *want to call* a company. :)

There areis often AI whichan AI voice that tells you your number in the queue.

Either "There is often an AI voice that tells you ..." or "There are often AI voices that tell you ..."

But when you' re finishingach the end of the queue, you're talking speak to a real person.

A president of thea call centre workers said in a podcast that she is worried about thait.

Indeed, AI is really a threat for call's centre workers.

But she thinks that an AI can't replace a real personople because peoplehumans are empathetic andwhile AI caisn't, because it doesn't have any consciousness.

Repeating "... because .... because ..." is confusing. You can divide up the sentence like:
"AI can't replace real people because humans are empathetic. AI isn't, since it doesn't have consciousness."

She also said that the purpose of the call's center workers consists by pacify theis to calm callers who are often angry and can shout dowon the phone.

Thanks for reading and. Please feel free to give adviceyour thoughts.

Please tell me howwhat you foundthink of my eEnglish!

or maybe you meant "how you found my post"? It appeared in my feed.

When you want to call a company, you often have to wait and be patient oin a queue.

Patient is an adjective, so you must "be" patient

There areis often an AI which tells you your number in the queue.

AI alone is singular, AIs is plural

But when you're finishingve reached the front of the queue, you're talking to a real person.

English considers a "queue" to be something to move through, so you start in the back of the queue, and move up to the front

AThe president of the call centre workers said in a podcast that she is worried about that.

"A president" is vague, "The president" is better

Indeed, AI is really a threat for call's center workers.

But she thinks that an AI can't replace a real person because people are empathetic and AI caisn't because it doesn't have any consciousness.

Keep the same verb (to be)

Yours could also be right if you add "AI can't be" therefore making it "to be" verb

She also said that the purpose of the call's workers consists byof pacifying the callers who are often angry and can shout down the pholine.

Line == term used for a telephone line (like a wire)