You get your ability to cast arcane spells back by resting through the mental rest, because of the mental focus required to shape those external energies. It takes a lot of willpower and focus to cast arcane spells, the mental rest and recuperation is what is important.
The idea that arcane magic comes from within is so absurd and breaks so much established D&D lore that it's not worth even giving serious thought to, it is to be dismissed out of hand as inherently ridiculous. Sorcerers have an innate talent for directing and channeling magical energy, but it's not from within them. Whoever wrote fluff saying otherwise, quite bluntly, was creating major contradictions in the lore.
The spell chapters seem mention the shaping external energies, but the part in the class descriptions feels a lot different...
"
Magic is a part of every sorcerer, suffusing body, mind, and spirit with a latent power that waits to be tapped. Some sorcerers wield magic that springs from an ancient bloodline infused with the magic of dragons.
Others carry a raw, uncontrolled magic within them, a chaotic storm that manifests in unexpected ways."
"Sorcerers are rare in the world, and it’s unusual to find a sorcerer who is not involved in the adventuring life in some way. People with
magical power seething in their veins soon discover that the power doesn’t like to stay quiet. A sorcerer’s magic wants to be wielded, and it has a tendency to spill out in unpredictable ways if it isn’t called on."
"An event in your past, or in the life of a parent or ancestor, left an indelible mark on you,
infusing you with arcane magic. This font of magic, whatever its origin, fuels your spells."
"Charisma is your spellcasting ability for your sorcerer spells, s
ince the power of your magic relies on your ability to project your will into the world."
"At 2nd level, you tap into
a deep wellspring of magic within yourself. This wellspring is represented by sorcery points, which allow you to create a variety of magical effects."