A strong emphasis on the quote is not always necessary; changing the rhythm with an italic style or increasing the font size relative to the body text is sufficient. If the quote has too much contrast at the expense of increased font size, it may distract from reading the main text. Although visually it may seem that a quote with more size of the text looks interesting and attractive.
There is no need to increase the font size of the quote. You can change the color of its text and make it bold. This will increase the contrast of the quote without having to increase the font size. This keeps the balance between the size of the text and the quote.
It's a great solution to add decorative elements to the quote. This helps draw attention to the quote without the need to increase its font size.
Creating a frame around the quote seems like a questionable solution, taking away the freedom of the quote and not solving practical goals. Emphasizing it with a light background might be more appropriate.
If the quote or its background extends beyond outside the text layout, it allows you to alternate the rhythm of the text interestingly and diversify the presentation of content.