I thought Prez in Vietname is more or less powerless position. Real power lies in the Central Military Commision and Party General Secretary just like China.
Supposedly, the top 3 role has almost the same power and that was how we keep dictator in check. All three positions are in the Central Military Commission.
China uses a different system, they have a designated paramount leader who holds two roles: President and Party Secretary, Vietnam doesn’t want to do that and kinda spreads the power out.
Why wasn't a new President nominated/ elected at the time? I'm pretty sure it was something as simple as dumb succession planning, unless you believe there is something more sinister with the death. Electing a new President in Vietnam is hard, there is a requirement of serving at least two terms in the Politburo before you can take one of the top three seats. Naturally, since it is a kind of up-or-out deal (you are old and very close to retirement age or exceeding it), the people who qualify are the one who are in the seats. And if one of them dies, you literally just runs out of candidates. Not to mention you need a party-wide electors meeting in addition to Congress meeting.
General Secretary is always the Secretary of the Central Military Commission, as the Vietnam People's Army swears absolute loyalty to the Communist party. That has nothing to do with the relative power between high ranking party official (it has obvious effect on the party's control of the military, but that is a different topic).