The part reading cannot teach you
Vocabulary and grammar go in through the eyes. Pronunciation does not. It is a physical skill, closer to learning an instrument than to learning a rule, and it is the reason people who read Portuguese comfortably can still be lost thirty seconds into a conversation.
Seven things below. The first three account for most of the distance between you and a Lisbon accent.
1. Unstressed vowels collapse
This is the single biggest marker. In Portugal, an e or an o that is not stressed thins out to a schwa (/ɨ/) or disappears completely.
Peixe has two e's. The first is stressed and clear; the second is barely there. What comes out is "paysh". Pronounce both and the word gets a lilt that immediately sounds foreign, or Brazilian.
The listening problem is the mirror image. Native speech has holes in it where you expect vowels, and your brain has to learn to fill them in rather than wait for them.
2. Nasal vowels
Portuguese has five, and English gives you nothing to build them from. The soft palate drops and air goes out through the nose and mouth at once.
The standard English-speaker error is to bolt an "ng" onto the end, turning pão into "pah-ng". There is a quick test: say the vowel while pinching your nose. If the sound dies, the air is going the right way.
3. The s that turns into sh
One letter, three jobs. Starting a word, it hisses: sol. Between vowels, it becomes a z: casa. At the end of a syllable or word, it goes to "sh".
As casas comes out as "ash cashash". Stack enough of those together and you have the sound that makes people say Portuguese reminds them of Russian, which it does, and for a reason that is genuinely phonetic rather than fanciful.
4. Open and closed vowels, which change the word
Spanish gives each vowel one sound and keeps its promise. Portuguese does not. A stressed vowel can be open (/ɛ/, /ɔ/, /a/) or closed (/e/, /o/, /ɐ/), and the difference is not decorative.
Sede with a closed first e is thirst. With an open one it is a headquarters. Same five letters, and often no accent mark to tell you which you are looking at, so the pattern has to be learned word by word and then by family: verbs tend to shift the vowel between the singular and the third-person plural, for instance.
5. Diphthongs glide, they do not step
Ai, ei, oi, and the nasal ones, ão and õe. Each is one movement, not two sounds in a row.
In peixe the "ei" should slide from /e/ up to /i/ without a seam. In pão you are moving from a nasal /ɐ̃/ into a nasalised /w̃/, and the commonest mistake is stopping halfway or letting it fall back into the throat.
6. Words run into each other
English leaves small gaps between words. Portuguese links them, and a final consonant will happily jump forward and start the next word.
Os amigos is not "osh amigos". It is "o-za-mee-goosh": the s becomes a z and moves house. Two identical vowels meeting will merge into one longer one.
This is the real source of the wall of sound. You are hunting for word boundaries and the language has stopped providing them. The fix is to stop hunting and start listening for whole rhythmic groups.
7. Stress-timing, which drives all of it
Spanish and Brazilian Portuguese give every syllable roughly equal time. European Portuguese keeps the gap between stressed syllables constant instead, whatever is in between.
Which means the unstressed syllables have to be raced through to make the timing work, and that is where the vowels get crushed. Everything above is downstream of this one fact. Try tapping the stressed beats while you listen; the words will start arriving in groups instead of as a stream.