The word 'negotiations' in this sentence is a mass noun. It can also be count, but here the speaker is referring to negotiations in general.
Some nouns can be both count and noncount. When they change from a count to a noncount noun, the meaning changes slightly. In the noncount form, the noun refers to the whole idea or quantity. In the count form, the noun refers to a specific example or type.
Source: academicguides.waldenu.edu
The definition of a mass noun is this:
a noun denoting something that cannot be counted (e.g. a substance or quality), in English usually a noun which lacks a plural in ordinary usage and is not used with the indefinite article, e.g. China, happiness
Source: Lexico
So here, 'the negotiations' is unnecessary and changes the meaning.
Regarding 'that', as you can see from this question and answer, it is used as a complimentiser and can be dropped from the sentence without changing meaning.