The modern German roman-type ß was developed at the end of the 19th century as an analogue of the blackletter ß, which was a ligature of ſ and z (which is reflected in its name) that had slowly acquired letter status and looked distinctively different from your ſs (more like ſʒ). Some of the new ß designs may have been inspired by your ſs and similar forms. However, at your time, no German letter ß with that form existed.
What you have in your text, is a ligature of the long s (ſ) and the round s (s). In my experience, in most languages there was considerable arbitrariness in the usage of s and ſ at that time.
What can be said for sure is that ſ was used at the beginning of words and s was used at the end. In every other case the distinction may depend on whether the s is located after the vowel of its syllable, at the end of a morpheme, and what letter is following it. The distinction may be also be covered by what was typographically nice or available¹. The blog Babelstone has a nice extensive survey of the usage of ſ and s in old texts.
As to why your author (or typesetter) decided to write ampliſsimo, cõſeſsui but eſſe and neceſſum is difficult to say without more example text. My best guess is that it was a fluke, arbitrary, or because the typesetter run out of one ligature glyph. However, it may also be that the writer considered that the ſs in ampliſsimo and cõſeſsui is positioned towards the end of a syllable or morpheme, while the ſſ in eſſe and neceſſum is not. The usage of eﬆ instead of eﬅ hints at a paradigm of that sort being employed here (in particular if ﬅ is used at the beginning of words). However, to arrive at a useful conclusion, you have to look at more example words.
Source: For my work on a blackletter font (see my profile) and a user-friendly and correct long-s rule set for the German language, I looked at various old texts in that regard and also consumed a lot of information on the history of the Germanletter ß. The aforementioned blog post should also confirm many things.
¹ e.g., there are English texts in which husband is written exactly like this, probably because the typesetter did not have an ſb ligature available and also wanted to avoid a large gap between ſ and b – which becomes evident through the word being hyphenated huſ-band.