The headline question has "Is God responsible...according to Romans 11:32?". So in this answer I want to stay in the grammar of Ro 11:32 and not stray into theological stances.
'has consigned'/synekleisen is aorist/indicative/active. Indicative/an objective fact. God has done it. He has consigned.
'may have mercy'/eleese is aorist/subjunctive/active. Subjunctive/potentially might. A contrast to indicative. A possibility.
This verse has a dramatic contrast between these two verbs: Objective fact all have been consigned contrasts with the possibility "may" be shown mercy.
'all'/pantas comes twice in this verse. It means the same in both cases. "All" are consigned to disobedience [in sin] and "all" are therefore in a state fromin which there is the potential of them beingthey potentially can be shown mercy.
Christians have a variety of belief systems. The grammar of this verse is clear. 'that he' God, has the possibility of showing mercy because firstly all were consigned to disobedience. Those to whom he does not show mercy will remain in the sin to which he consigned them.
[Compatibilists would say that God's sovereignitysovereignty was compatible with free-will. That's a big topic. Ro 11:32 is undiluted God's sovereignity]sovereignty]