Engagement:
The more romantic the conversation, the higher the chance that one Sim will propose to another.
There is little likelihood that an inspired character might propose an engagement, but the largest percentage is still directed to the romantically inclined.
When the conversation isn't going well, no one will suggest anything on their own.

Example: During a flirtatious conversation, the chance is significantly higher than during everyday conversations. Accordingly, a flirtatious mood and flirting are more likely to dispose characters to take decisive steps.
Disagreements:

Cancellation of a previously concluded engagement, as well as a request to remain friends, will occur depending on the mood.
When your partner is upset or angry, your Sim should try to calm them down. In cases where the buff is strong enough (presumably +2, +3), the character can break the relationship. The situation is similar with discomfort and boredom.
The rest of the emotional states should not cause concern. (Happy, playful, considerate, etc.)

Also, disagreements are possible during conversations that cause negative moodlets: boredom, embarrassment, sadness, anger. Conversational insults are more likely to cause your partner to ditch your Sim.

Traits:
As you might have guessed, the above is directly related to the character of the sim. The chances of getting an offer from "Romantic", "Family Man" are much greater than from "Impatient" or "Fickle". It is worth noting that the relationship with the "Wicked", "Bully" and "Sad" will be difficult, this applies no less to other features that give temporary negative moodlets.

No romance in the sentences - it is not autonomous, i.e. only you can force a sim to propose. The possibility of rejection still remains.

This option modifies certain interactions. Now all your Sims have to do is get romantically attracted, and an engagement proposal can be made before they become a couple.

At the same time, the connection between the actions "Become a couple" and "Get married" remains. Accordingly, in order to get married properly, you will first need to become a couple, even if you have passed the engagement stage.