I'm not sure I understand your question? 'the newspaper' is tidningen, and 'a/one newspaper' is en tidning.
A vowel followed by a single consonant is (almost) always pronounced long in Swedish unless it is the last vowel in the word, in which case it can be either.
In the case of the word man, it actually has two meanings, with the short a sound it means "man", but with the long a sound it means "mane".
So, when we add "en" to the end, the a is no longer the last vowel and we also have to add a second consonant to preserve the short a sound.
Mannen - the man. (short a)
Manen - the mane. (long a)
The TTS pronounces "läser" a bit like "leser", I find. Is it in this case standard or a bit more like Stockholm accent?
Apparently läser should be pronounced slightly different to the way the TTS says it