Swedish Livonia was a province created from territories that were ceded by the Commonwealth in 1629. This territory remained under de facto Swedish rule until 1710 and was ceded formally in 1721. Parts of this territory (which evidenced changes in borders) were inherited from Denmark after Brömsebro. What I am wondering about is whether the Swedes during this time discussed the proper fortification of this frontier with Russia—both Finland, Ingermanland, and Estonia were far better fortified towards the east while I have not seen any proof that similar plans were carried out in Swedish Livonia.
For a better rephrasing of my question: Did the Swedish seriously consider (i.e., try to allocate money, get proposals passed in the Riksdag, etc) the benefits of fortifying Swedish Livonia, especially in the south and east? Why did they not fortify these frontiers, including the approaches to Riga?
As a comparison, Swedish Finland was defended by Vyborg and Kexholm which were modernized during the 17th century. Swedish Ingria was defended by Nyenskans and Nöteborg. Swedish Estonia's Reval and Narva were both refortified during the 17th century (with Narva later acting as the capital of Ingermanland). In Livonia, Sweden refortified Pernau and Dorpat—in the north of the province—as well as built a system of bastions around Riga, along with an additional fort in the mouth of the Daugava (Neumünde). Further, the Swedes inherited Arensburg which the Danish had modernized into a baston-fortress during their rule.
Instinctively, these moves in Livonia don't make much sense: the Baltic Sea side was heavily defended while the inland parts were not. The Swedish fleet was, at the time, one of the primary forces on the Baltic Sea as well (with no Russian competition, but the Commonwealth, Denmark, and some German principalities acting as the other forces). The defensive value of Dorpat for example in this time should have been relatively small (despite Gustav Adolf founding an university in this town, it looks as if the mercantile importance of the town was rather on the decrease in this time).
Riga was (depending on the sources) either the largest or the second-largest town in Sweden. Yet, it's defense—especially coming downstream the Daugava—seems to have been left only to the city's own defenses. It is perhaps notable that Imperial Russia later built impressive fortifications in Daugavpils as well as modernized Riga's defenses even more.
Rönneburg which is described on the above map was rebuilt as a town during Swedish times, but the fortifications were actually disbanded. Neuhausen seems to have formed an important part of the defense of the eastern frontier, but there are no notices of the area's defenses being improved during this time period that I've found though the old Medieval castle was besieged and taken numerous times by the Poles, Russians, and Swedes during the 17th century wars.
The article on Neumünde mentions a military map from 1653 which could be helpful but there are no links to it:
By 1653 a map issued by Swedish Military council showed that the Dünamünde fortress was destroyed and the Daugavgrīva castle was in ruins.
Also, to cover all bases, prior to Swedish rule the Polish re-used old Medieval castles as the centres of their starostships and vojvodships. The map on that link mentions numerous towns, none of which in the Wenden vojvodship were (seemingly) fortified by the Swedish. Moreover, many previous frontier-castles, like Marienhausen, were allowed to lapse during this time. While the English article describes how it was destroyed in 1702, the Estonian one goes further to not note any constructions during the Swedish period.
The above is perhaps especially notable as in the Russo-Swedish War (1656–1658) the Russians managed to overrun the dilapidated defenses of Daugavpils and Kokenhusen, and were only stopped at Riga which was partially modernised. They had clearly been coming down the route of the Daugava. Yet, even after this war, there is nothing apparent that would demonstrate Sweden considering defensive upgrades in the east of Swedish Livonia.
@TomAU's answer made me investigate another avenue. Erik Dahlbergh, the Swedish Vauban, is described in his Estonian WP article to have promoted the greater fortification of the eastern border but was overruled by Karl XI who wanted the Danish border secured—but this is unsourced. It adds that Karl XII approved the further fortification of the east (without details as to where and what) but there wasn't enough time for this before the start of the Great Northern War.