(Using Blender 3.6.8)
Objective
To superimpose some cumulative randomness to a deterministic displacement.
The animation above shows a triangle animated with a uniform translation, and a decorrelated moving square put at the front of a random walk on a grid. Suzanne motion is a linear combination of both, with weighted contribution of randomness. It is to notice that Suzanne is not wandering away from the triangle, even if the random front is far from its starting position.
The animation below illustrates what could be achieved with a simulated Brownian motion instead of a random walk on a grid.
Approach
To detail the explanation, the process is split in many objects, some with dedicated GeometryNodes modifiers.
1. Deterministic Walker (Prism):
1.1. Its position is animated by inserting keyframes after moving it, at frames 1 and 250 for the demonstration.
1.2. Using the Graph Editor, a Linear Interpolation Mode is set for all three coordinates.
2. Random Path & Path (Lattice):
2.1. The random walk on a grid is built with a GeometryNodes modifier based on a Simulation Zone, and it is manipulated as an independent Mesh.
2.2. For the demonstration, the "Path" object is just giving some volume to the "Random Path" object to render it.
3. Random Walker (Cube):
3.1. To track the front of the random walk and to access its displacement, a GeometryNodes modifier is attached to an object "exposing" its position for other objects to read.
3.2. For the demonstration a Cube is used, but a Single Vertex should be favoured if only one single position has to be "exposed".
4. Walker (Suzanne):
4.1. A GeometryNodes modifier is attached to the object to animate. Its inputs are:
4.1.1. The weight scaling the random contribution.
4.1.2. Both walkers, random and deterministic.
4.2. The Location of the deterministic walker is recovered through an Object Info node.
4.3. The Position of the first vertex (i.e. with Index 0) of the random walker is recovered by a Sample Index node set in Point domain.
4.4. A weighted linear combination is computed by a Multiply Add math node.
4.5. The origin of the object is not modified, only its vertices position with a Transform Geometry node.
NB: Obviously for final rendering, all these objects should be hidden except the Walker (i.e. Suzanne for the demonstration).
Random path and walker
1. The path is made of adjacent edges added using a Join Geometry node, one at a time inside a Simulation Zone.
2. Such an edge is built with a Mesh line node with just two points:
2.1. The first end point position is recovered from the previous frame through the Prev input socket, initialized as (0,0,0) at frame 1. A Sample Index node is required to get a single position, independent of how many points are in the recycled Geometry. To do so, its Index socket is hardcoded to 0.
2.2. The second end point position is defined by an Offset. Consequently, its value is captured after the Mesh line node by a Sample Index node with Index set to 1, to be transferred to the next frame.
3. (dark red frame) To simulate a random walk on a grid, the offset is drawn from a "lookup table" using a Sample Index node:
3.1. Four vertices at cardinal directions are generated by a Mesh Circle node set with a unitary Radius.
3.2. A random integer between 0 and 3 is drawn with a Random Value node whom Seed is changing with the Frame count recovered through a Scene Time node. It is to notice that the ID input socket is hardcoded to 0 to get a single random value.
4. (dark green frame) To simulate a Brownian motion (i.e. the limit of a random walk when the step size goes to zero), the offset is drawn with a Random Value node with Data Type set to Vector.
5. Because a random walk might drift significantly before a very large number of steps is made to get a statistically centred distribution, the current path is centred at every frame, outside of the Simulation Zone:
5.1. The centre of its Bounding Box is computed as the average between Min and Max corners position.
5.2. This vector is subtracted from every vertex position using the Translation of a Transform Geometry node. So the origin of the object is not affected, but its points are moved "around" its origin.
1. To "expose" the location of the random path front at each frame, the above GeometryNodes modifier is attached to an object with at least one vertex, if only one vector must be exposed. NB: If more information must be exposed, other vertices of the same object can be used to encode more data by adapting this graph.
2. The Geometry of the random path is recovered through an Object Info node.
3. By construction, the front is the last point. Its index is computed by subtracting 1 to the number of points recovered through a Domain Size node.
4. From this Index, a Sample Index node is used to get the front Position, that can be scaled with the Randomness user-defined parameter.
5. This vector is used to shift the "exposing" object using a Transform Geometry node. NB: Consequently, the exact front position might not be transferred. If this is a requirement, a Set Position node should be used instead.
How to use it
The "Random Walker" GeometryNodes modifier can be attached directly to an object with keyframed "deterministic" transformations, without using an intermediate "observer" and a weighted linear combination. Other randomized Paths can be added to make noise on rotation and scaling.
Resources
Path Renderer
1. To visualize the random path, edges are converted to curves, to transform these to cylinders using a classical Mesh to Curve & Curve to Mesh nodes sequence.
2. It is to notice that to reduce the resulting mesh size, a Merge by Distance node is inserted after the path Geometry is recovered through an Object Info node. This node is not incorporated in the path builder GN graph as it is reordering vertices. Consequently, the last point might not be the path front when backtracking occurs.
Blender file: 
