On the subject of the immortality of the soul, Martin Luther has this to say :
For since we call it a sleep, we know that we shall not remain in it, but be again awakened and live, and that the time during which we sleep, shall seem no longer than if we had just fallen asleep. Hence, we shall censure ourselves that we were surprised or alarmed at such a sleep in the hour of death, and suddenly come alive out of the grave and from decomposition, and entirely well, fresh, with a pure, clear, glorified life, meet our Lord and Savior Jesus Christ in the clouds.
Martin Luther and William Tyndale on the State of the Dead
John Calvin exhorts not to enquire into matters that are not revealed but what he does say is this :
Many greatly torment themselves with discussing what place they occupy, and whether or not they already enjoy celestial glory. It is foolish and rash to inquire into hidden things, farther than God permits us to know. Scripture, after telling that Christ is present with them, and receives them into paradise (John 12:32), and that they are comforted, while the souls of the reprobate suffer the torments which they have merited goes no farther. What teacher or doctor will reveal to us what God has concealed?
As to the place of abode, the question is not less futile and inept, since we know that the dimension of the soul is not the same as that of the body. When the abode of blessed spirits is designated as the bosom of Abraham, it is plain that, on quitting this pilgrimage, they are received by the common father of the faithful, who imparts to them the fruit of his faith. Still, since Scripture uniformly enjoins us to look with expectation to the advent of Christ, and delays the crown of glory till that period, let us be contented with the limits divinely prescribed to us--viz. that the souls of the righteous, after their warfare is ended, obtain blessed rest where in joy they wait for the fruition of promised glory, and that thus the final result is suspended till Christ the Redeemer appear.
There can be no doubt that the reprobate have the same doom as that which Jude assigns to the devils, they are "reserved in everlasting chains under darkness unto the judgment of the great day," (Jude ver. 6).
Calvin's Institutes - Book 3 - Chapter 25
It is quite clear that neither Luther nor Calvin accepted the idea of the annihilation of the soul, in any way or for any reason, nor did they accept the possibility (whether temporarily or permanently) of the 'cessation of existence'.
A more clear text, regarding immortality, than the two quoted (the two quoted texts are not definitive in respect of the topic under inquiry) is the last verse of Isaiah, 66:24, which is quoted by Jesus and reported by Mark :
... to go into hell, into the fire that never shall be quenched: Where their worm dieth not, and the fire is not quenched. [Mark 9:43,44 KJV]
Writing of this text Gill says the following in his commentary :
This will be always the case; conscience will be ever distressing, racking, and torturing them; it will never cease, nor cease doing this office, and so the Chaldee paraphrase of Isaiah 66:24 renders this phrase, , "their souls shall not die"; but shall ever continue in the dreadful torments and unspeakable horrors of a corroding conscience; and by "the fire" may be meant the fire of divine wrath let into their souls, which will never be extinguished; and so Jarchi interprets the phrase in Isaiah 66:24, "their fire", "in hell".
Gill's Commentary - Biblehub