I have tried to do some research but most of them show CSS3 and the
d:path CSS method does not work either and is actually worse because
nothing shows up.
Please see browser support d: path animations.
Unfortunately, this does not work in the specified browsers, including Safari.
Let's hope to see better support in the near future.
This answer will not solve your problem with CSS3 path animations as it is not possible, but it will make it easier with SVG animations that work in all modern browsers, including Safari.
Specifying path data: the d property:
For animation, two d property values can only be interpolated smoothly
when the path data strings contain have the same structure, (i.e.
exactly the same number and types of path data commands which are in
the same order). If an animation is specified and the lists of path
data commands do not have the same structure, then the values must be
interpolated using the discrete animation type.
To fulfill these requirements, you can use this technique
Step #1
First you need to get the shape of the curve at the starting position:

Step #2
Then, by moving the anchor points of the curve in the vector editor, we get the final shape of the curve:

Step #3
Next, we write a command to animate the curve:
<animate attributeName="d" values="path1;path2;path1" />, where
path1 - Curve shape at the start
path2 - Finish curve shape
as @Kaiido said in the comments try not to allow extra spaces before the semicolon
svg {
width:40%;
height:40%;
}
path {
fill:#2F3136;
stroke:black;
stroke-width:4;
}
<svg xmlns:svg="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg" version="1.1" width="770" height="770" viewBox="0 0 770 770" preserveAspectRatio="xMinYMin meet" >
<path d="M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z" >
<animate attributeName="d"
dur="4s"
values="
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 76.8 2.3 110.7-24.2 67.7-52.9 94.4-1.3 137.3-18.5 40.1-16.1 39.1-57.3 105-76.1 93.8-26.8 81.5-74.9 124.6-109.6 22.3-17.9 50.6-23.4 69.2-50.8 41.5-61.1 14.5-80.4 66.9-115.4 0 0 28.1-21.9 36.9-36.9 16.5-28.3 27.7-30.3 26.5-94.6-0.4-21.7 2.5-76.9 19.6-94.6C730.2 67.3 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z"
repeatcount="indefinite"
/>
</path>
</svg>
- Option with background image and shadow
.container {
width:75%;
height:75%;
}
path {
fill:#2F3136;
stroke:black;
stroke-width:0;
fill-opacity:0.5;
-webkit-filter: drop-shadow(4px 4px 1px black);
filter: drop-shadow(4px 4px 1px black);
}
<div class="container">
<svg xmlns:svg="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 770 770" preserveAspectRatio="none" >
<image xlink:href="https://i.stack.imgur.com/ABxSm.jpg" x="10" width="1125px" height="750px" >
</image>
<path d="M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z" >
<animate id="an_d" attributeName="d"
dur="6s"
begin="0s"
values="
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 76.8 2.3 110.7-24.2 67.7-52.9 94.4-1.3 137.3-18.5 40.1-16.1 39.1-57.3 105-76.1 93.8-26.8 81.5-74.9 124.6-109.6 22.3-17.9 50.6-23.4 69.2-50.8 41.5-61.1 14.5-80.4 66.9-115.4 0 0 28.1-21.9 36.9-36.9 16.5-28.3 27.7-30.3 26.5-94.6-0.4-21.7 2.5-76.9 19.6-94.6C730.2 67.3 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z"
repeatCount="indefinite"
/>
</path>
</svg>
</div>
- Border animation plus whole block size animation
.container {
width:75%;
height:75%;
}
path {
fill:#2F3136;
stroke:black;
stroke-width:0;
fill-opacity:0.5;
}
<div class="container">
<svg xmlns:svg="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg" version="1.1" viewBox="0 0 770 770" preserveAspectRatio="none" >
<defs>
<filter id='shadow'>
<feGaussianBlur in='SourceAlpha' stdDeviation='2' />
<feOffset dx='3' dy='3' result='blur' />
<feMerge>
<feMergeNode in='blur' />
<feMergeNode in='SourceGraphic' />
</feMerge>
</filter>
</defs>
<image xlink:href="https://i.stack.imgur.com/ABxSm.jpg" x="10" width="1125px" height="750px" >
</image>
<path filter="url(#shadow)" d="M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z" >
<animate id="an_d" attributeName="d"
dur="6s"
begin="0s;an_t.end"
values="
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 76.8 2.3 110.7-24.2 67.7-52.9 94.4-1.3 137.3-18.5 40.1-16.1 39.1-57.3 105-76.1 93.8-26.8 81.5-74.9 124.6-109.6 22.3-17.9 50.6-23.4 69.2-50.8 41.5-61.1 14.5-80.4 66.9-115.4 0 0 28.1-21.9 36.9-36.9 16.5-28.3 27.7-30.3 26.5-94.6-0.4-21.7 2.5-76.9 19.6-94.6C730.2 67.3 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z;
M8.1 1.2V721.6c0 0 73.2 20.7 105 16.1 39.9-5.6 63.5-61.7 105-66.9 35-4.4 74.9 1 105-13.8 41.9-20.7 60.2-90.1 92.3-108.4 30.9-17.7 74.9-13.9 101.5-33.5 63.3-46.3 5.3-81.5 76.1-145.3 0 0 47.9-24.3 61.1-46.1 19.6-32.3 18.5-61.6 18.5-111.9 0-21.7 15.2-38.8 32.3-56.5C730.2 121.6 752.7 68.8 719.8 2.9 516.8-0.6 218-0.6 8.1 1.2Z"
repeatcount="1"
/>
<animateTransform id="an_t" attributeName="transform" type="scale" dur="12s" begin="an_d.end" values="1;0.5;0.5;1" />
</path>
</svg>
</div>